Calculus

Problem 4601

Find $d y / d x$ if (1) $y=\frac{e^{4 x^{2}+2 x}}{2 x+1}$

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Problem 4602

Find the limit: $\lim _{x \rightarrow 1} \frac{x}{\ln x}$ .

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Problem 4603

Find the limit: $\lim _{x \rightarrow e}(x \ln x - x)$ .

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Problem 4604

Calculate the limit: $\lim _{x \rightarrow e}(x \ln x - x)$

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Problem 4605

Find the limit: $\lim _{x \rightarrow 0} \ln \left(e^{x+1}\right)$ .

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Problem 4606

Find the limit: $\lim _{x \rightarrow \infty} \frac{x+1}{\sqrt{4 x^{2}+2}}$ .

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Problem 4607

Find the velocity function $v(t)$ for the hummingbird's position $s(t)=-10 t^{3}-t-6$ in feet.

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Problem 4608

Find the area of the region enclosed by the curves $y=2 \cos x$ and $y=2 \cos 2 x$ for $0 \leq x \leq \pi$ .

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Problem 4609

Find $\frac{d y}{d x}$ of the following finctions: if $y=2 \cos 2 x-1$

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Problem 4610

Find $\frac{d y}{d x}$ of the following function (1) if $y=\frac{x^{2}}{x+1}$

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Problem 4611

Defferentiate with respect to $x: 4-x^{2}$

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Problem 4612

Find $d y / d x$ by implicit differentiation $x^{3} y^{5}+3 x=8 y^{3}+1$

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Problem 4613

If $f(x, y)=2 x^{2}-y e^{y}$ and the maximum rate of change of $f$ at $(1,0)$ is $a$ then $a^{2}$ equal
Answer: $\square$

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Problem 4614

If $f(x, y)=2 x^{2}-y e^{y}$ and the maximum rate of change of $f$ at $(1,0)$ is $a$ then $a^{2}$ equal
Answer: $\square$

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Problem 4615

Given $\vec{F}=4 \hat{i}+5 \hat{j}-6 y \hat{k}$ . Find $\oint \vec{F} \cdot \overrightarrow{d l}$ going around the loop that starts from the point $(0,0,0)$ to the point $(0,0,4)$ then to the point $(0,1,4)$ then to the point $(0,1,0)$ and back to $(0,0,0)$ . a. 4 b. -4 c. 24 d. 0 e. -24

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Problem 4616

Given $\vec{F}=4 \hat{i}+5 \hat{j}-6 y \hat{k}$ . Find $\oint \vec{F} \cdot \overrightarrow{d l}$ going around the loop that starts from the point $(0,0,0)$ to the point $(0,0,4)$ then to the paint $(0,1,4)$ then to the point $(0,1,0)$ and back to $(0,0,0)$ . a. -4 b. -24 c. 0 d. 24 e. 4
Clear my choice

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Problem 4617

Exercice $\mathrm{n}^{\circ} 9$ : Soit $a \in] 0,1$ . Montrer à l'aide des accroissements finis que pour tout $n \in \mathbb{N}^{*}$ , $\frac{a}{(n+1)^{1-a}} \leqslant(n+1)^{a}-n^{a} \leqslant \frac{a}{n^{1-a}} .$

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Problem 4618

Determine if the car is moving left or right at $t=8$ for the function $s(t)=-4 t^{3}-10 t^{2}+t-4$ .

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Problem 4619

Find the acceleration function $a(t)$ for the particle with position $s(t)=-3t^{2}-t+1$ (in meters) at time $t$ .

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Problem 4620

Find the acceleration of the particle at $t=3$ seconds for the function $s(t)=t^{3}-3 t^{2}-8 t+1$ . Answer in $\mathrm{ft} / \mathrm{s}^{2}$ .

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Problem 4621

Determine if the train, described by $s(t)=t^{4}-2 t^{3}-5 t^{2}+3$ , is speeding up or slowing down at $t=2$ seconds.

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Problem 4622

Find the interval(s) where the hummingbird slows down for $s(t)=-t^{3}+9 t^{2}-24 t-4$ , $t \geq 0$ .

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Problem 4623

Make $x$ the subject of $\frac{d x}{t}=m$

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Problem 4624

Exercice 3 ( 06 points) 3 kg d'air à la température de $20^{\circ} \mathrm{C}$ et sous une pression de 2 bar sont comprimes pusqua las pression de 10 bar.
Déterminer la variation de l'énergie interne, le travail de compression et la quantité de chaleur échangée au cours de l'évolution, pour les trois cas suivants :
1. Compression isotherme.
2. Compression adiabatique.
التمرين
3. Compression polytropique ( $n=1,3$ ).
صنة دة د.إلهام بن عمر On suppose que l'air est un gaz parfait. ( $C_{\mathrm{v}}=714 \mathrm{~J} \cdot \mathrm{~kg}^{-1} \cdot \mathrm{~K}^{-1}$ et $\left.\mathrm{R}=0,287 \mathrm{~kJ}^{-} \cdot \mathrm{kg}^{-1} \cdot \mathrm{~K}^{-1}\right)$
Réponses 3 \begin{tabular}{|c|c|c|} \hline & Expressions littérales & Résultats numériques \\ \hline \multirow{3}{}{Compression isotherme} & $\Delta U=$ & $\Delta \mathrm{U}=$ \\ \hline & & W = \\ \hline & $\mathrm{Q}=$ & $Q=.!$ \\ \hline \multirow{3}{}{Compression adiabatique} & $\Delta \mathrm{U}=-$ & $\Delta \mathrm{U}=$ \\ \hline & & $\mathrm{W}=$ \\ \hline & $Q=$ & $\mathrm{Q}=$ \\ \hline \multirow{3}{*}{Compression polytropique} & $\Delta \mathrm{U}=$ & $\Delta \mathrm{U}=$ \\ \hline & $\mathrm{W}=$ & w = \\ \hline & $\mathrm{Q}=$ & $\mathrm{Q}=$ \\ \hline \end{tabular}

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Problem 4625

Find the limit $\lim _{x \rightarrow a}\left\{[h(x)]^{2}-f(x) g(x)\right\}$ given $\lim _{x \rightarrow a} f(x)=3$ , $\lim _{x \rightarrow a} g(x)=5$ , $\lim _{x \rightarrow a} h(x)=-2$ .

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Problem 4626

Find the interval(s) where the car moves left for $s(t)=-t^{3}+6 t^{2}+36 t+4$ with $t \geq 0$ .

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Problem 4627

Find the ball's velocity when it first reaches $880 \mathrm{ft}$ , given $s(t)=-16 t^{2}+256 t$ .

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Problem 4628

3). Evaluate by changing of the ordrof integration. (a) $\int_{0}^{2} \int_{1}^{e^{x}} d y d x$ (b) $\int_{0}^{1} \int_{x^{2}}^{2-x} x y d x d y$ (c) $\int_{0}^{4 a} \int_{x / 4 a}^{2 \sqrt{a x}} d y d x$ .

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Problem 4629

$f(x)=x e^{x}-x$ is concave up ou?

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Problem 4630

8. If $f(x)=\left\{x^{2}+3\right.$ (A) $a=1, b=3$ (B) $\frac{1}{7}$ (C) $\frac{1}{3}$ (D) $\frac{1}{3}$ (B) $\left.a=\begin{array}{c}x<0 \\ 3, b=0\end{array}\right\}$ and $f(x)$ is differentiable at $x=0$ , then: (C) $a=3, b=1$ (D) $a=0, b=3$ $\begin{array}{lll}\text { (A) } x=\ln 2 & \text { (B) } x=\ln 5 & \text { (C) } x=\ln 3\end{array}$ (D) $x=2 \ln 5$

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Problem 4631

$\qquad$ (D) $y=0$

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Problem 4632

- A është vlerësues i pazhvendosur? Pse? 5.24. Shqyrtojmë shpërndarjen eksponenciale të zhvendosur me densitet $f(x)=\lambda e^{-\lambda(x-s)}$ $k u X \geq 5$ . Gjeni me anë të metodës së përgjasisë maksimale një vlerësues për $\lambda$ ?

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Problem 4633

B) If the function $f(x)=a x^{3}-3 x^{2}+b x+c$ has a local minimum at -5 and a local maximum at $x=\frac{-1}{2}$ and inflection point at $x=\frac{1}{4}$ find $a, b, c \in R$ .

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Problem 4634

Q3: A) Let M be a point moving on the curve $y^{2}=x^{3}$ such that rate of change the point $M$ getting away from of the origin point is 4 unit $/ \mathrm{s}$ . Find the rate of chang of the x -coordinate for M when $x=2$

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Problem 4635

$\lim _{x \rightarrow 0^{+}} x-1-\frac{2 \ln x^{2}}{\sqrt{x}}$

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Problem 4636

$\int_{0}^{1} \int_{0}^{y^{2}} \sqrt{1+y^{3}} d x d y$

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Calculus

Problem 4601

Find dy/dxd y / d xdy/dx if (1) y=e4x2+2x2x+1y=\frac{e^{4 x^{2}+2 x}}{2 x+1}y=2x+1e4x2+2x​

Problem 4602

Find the limit: lim⁡x→1xln⁡x\lim _{x \rightarrow 1} \frac{x}{\ln x}limx→1​lnxx​.

Problem 4603

Find the limit: lim⁡x→e(xln⁡x−x)\lim _{x \rightarrow e}(x \ln x - x)limx→e​(xlnx−x).

Problem 4604

Calculate the limit: lim⁡x→e(xln⁡x−x)\lim _{x \rightarrow e}(x \ln x - x)limx→e​(xlnx−x)

Problem 4605

Find the limit: lim⁡x→0ln⁡(ex+1)\lim _{x \rightarrow 0} \ln \left(e^{x+1}\right)limx→0​ln(ex+1).

Problem 4606

Find the limit: lim⁡x→∞x+14x2+2\lim _{x \rightarrow \infty} \frac{x+1}{\sqrt{4 x^{2}+2}}limx→∞​4x2+2​x+1​.

Problem 4607

Find the velocity function v(t)v(t)v(t) for the hummingbird's position s(t)=−10t3−t−6s(t)=-10 t^{3}-t-6s(t)=−10t3−t−6 in feet.

Problem 4608

Find the area of the region enclosed by the curves y=2cos⁡xy=2 \cos xy=2cosx and y=2cos⁡2xy=2 \cos 2 xy=2cos2x for 0≤x≤π0 \leq x \leq \pi0≤x≤π.

Problem 4609

Find dydx\frac{d y}{d x}dxdy​ of the following finctions: if y=2cos⁡2x−1y=2 \cos 2 x-1y=2cos2x−1

Problem 4610

Find dydx\frac{d y}{d x}dxdy​ of the following function (1) if y=x2x+1y=\frac{x^{2}}{x+1}y=x+1x2​

Problem 4611

Defferentiate with respect to x:4−x2x: 4-x^{2}x:4−x2

Problem 4612

Find dy/dxd y / d xdy/dx by implicit differentiation x3y5+3x=8y3+1x^{3} y^{5}+3 x=8 y^{3}+1x3y5+3x=8y3+1

Problem 4613

If f(x,y)=2x2−yeyf(x, y)=2 x^{2}-y e^{y}f(x,y)=2x2−yey and the maximum rate of change of fff at (1,0)(1,0)(1,0) is aaa then a2a^{2}a2 equalAnswer: □\square□

Problem 4614

If f(x,y)=2x2−yeyf(x, y)=2 x^{2}-y e^{y}f(x,y)=2x2−yey and the maximum rate of change of fff at (1,0)(1,0)(1,0) is aaa then a2a^{2}a2 equalAnswer: □\square□

Problem 4615

Problem 4616

Problem 4617

Problem 4618

Determine if the car is moving left or right at t=8t=8t=8 for the function s(t)=−4t3−10t2+t−4s(t)=-4 t^{3}-10 t^{2}+t-4s(t)=−4t3−10t2+t−4.

Problem 4619

Find the acceleration function a(t)a(t)a(t) for the particle with position s(t)=−3t2−t+1s(t)=-3t^{2}-t+1s(t)=−3t2−t+1 (in meters) at time ttt.

Problem 4620

Find the acceleration of the particle at t=3t=3t=3 seconds for the function s(t)=t3−3t2−8t+1s(t)=t^{3}-3 t^{2}-8 t+1s(t)=t3−3t2−8t+1. Answer in ft/s2\mathrm{ft} / \mathrm{s}^{2}ft/s2.

Problem 4621

Determine if the train, described by s(t)=t4−2t3−5t2+3s(t)=t^{4}-2 t^{3}-5 t^{2}+3s(t)=t4−2t3−5t2+3, is speeding up or slowing down at t=2t=2t=2 seconds.

Problem 4622

Find the interval(s) where the hummingbird slows down for s(t)=−t3+9t2−24t−4s(t)=-t^{3}+9 t^{2}-24 t-4s(t)=−t3+9t2−24t−4, t≥0t \geq 0t≥0.

Problem 4623

Make xxx the subject of dxt=m\frac{d x}{t}=mtdx​=m

Problem 4624

Problem 4625

Problem 4626

Find the interval(s) where the car moves left for s(t)=−t3+6t2+36t+4s(t)=-t^{3}+6 t^{2}+36 t+4s(t)=−t3+6t2+36t+4 with t≥0t \geq 0t≥0.

Problem 4627

Find the ball's velocity when it first reaches 880ft880 \mathrm{ft}880ft, given s(t)=−16t2+256ts(t)=-16 t^{2}+256 ts(t)=−16t2+256t.

Problem 4628

Problem 4629

f(x)=xex−xf(x)=x e^{x}-xf(x)=xex−x is concave up ou?

Problem 4630

Problem 4631

\qquad (D) y=0y=0y=0

Problem 4632

Problem 4633

B) If the function f(x)=ax3−3x2+bx+cf(x)=a x^{3}-3 x^{2}+b x+cf(x)=ax3−3x2+bx+c has a local minimum at -5 and a local maximum at x=−12x=\frac{-1}{2}x=2−1​ and inflection point at x=14x=\frac{1}{4}x=41​ find a,b,c∈Ra, b, c \in Ra,b,c∈R.

Problem 4634

Q3: A) Let M be a point moving on the curve y2=x3y^{2}=x^{3}y2=x3 such that rate of change the point MMM getting away from of the origin point is 4 unit /s/ \mathrm{s}/s. Find the rate of chang of the x -coordinate for M when x=2x=2x=2

Problem 4635

lim⁡x→0+x−1−2ln⁡x2x\lim _{x \rightarrow 0^{+}} x-1-\frac{2 \ln x^{2}}{\sqrt{x}}limx→0+​x−1−x​2lnx2​

Problem 4636

∫01∫0y21+y3dxdy\int_{0}^{1} \int_{0}^{y^{2}} \sqrt{1+y^{3}} d x d y∫01​∫0y2​1+y3​dxdy

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Find $d y / d x$ if (1) $y=\frac{e^{4 x^{2}+2 x}}{2 x+1}$

Find the limit: $\lim _{x \rightarrow 1} \frac{x}{\ln x}$ .

Find the limit: $\lim _{x \rightarrow e}(x \ln x - x)$ .

Calculate the limit: $\lim _{x \rightarrow e}(x \ln x - x)$

Find the limit: $\lim _{x \rightarrow 0} \ln \left(e^{x+1}\right)$ .

Find the limit: $\lim _{x \rightarrow \infty} \frac{x+1}{\sqrt{4 x^{2}+2}}$ .

Find the velocity function $v(t)$ for the hummingbird's position $s(t)=-10 t^{3}-t-6$ in feet.

Find the area of the region enclosed by the curves $y=2 \cos x$ and $y=2 \cos 2 x$ for $0 \leq x \leq \pi$ .

Find $\frac{d y}{d x}$ of the following finctions: if $y=2 \cos 2 x-1$

Find $\frac{d y}{d x}$ of the following function (1) if $y=\frac{x^{2}}{x+1}$

Defferentiate with respect to $x: 4-x^{2}$

Find $d y / d x$ by implicit differentiation $x^{3} y^{5}+3 x=8 y^{3}+1$

If $f(x, y)=2 x^{2}-y e^{y}$ and the maximum rate of change of $f$ at $(1,0)$ is $a$ then $a^{2}$ equal
Answer: $\square$

If $f(x, y)=2 x^{2}-y e^{y}$ and the maximum rate of change of $f$ at $(1,0)$ is $a$ then $a^{2}$ equal
Answer: $\square$

Determine if the car is moving left or right at $t=8$ for the function $s(t)=-4 t^{3}-10 t^{2}+t-4$ .

Find the acceleration function $a(t)$ for the particle with position $s(t)=-3t^{2}-t+1$ (in meters) at time $t$ .

Find the acceleration of the particle at $t=3$ seconds for the function $s(t)=t^{3}-3 t^{2}-8 t+1$ . Answer in $\mathrm{ft} / \mathrm{s}^{2}$ .

Determine if the train, described by $s(t)=t^{4}-2 t^{3}-5 t^{2}+3$ , is speeding up or slowing down at $t=2$ seconds.

Find the interval(s) where the hummingbird slows down for $s(t)=-t^{3}+9 t^{2}-24 t-4$ , $t \geq 0$ .

Make $x$ the subject of $\frac{d x}{t}=m$

Find the interval(s) where the car moves left for $s(t)=-t^{3}+6 t^{2}+36 t+4$ with $t \geq 0$ .

Find the ball's velocity when it first reaches $880 \mathrm{ft}$ , given $s(t)=-16 t^{2}+256 t$ .

$f(x)=x e^{x}-x$ is concave up ou?

$\qquad$ (D) $y=0$

B) If the function $f(x)=a x^{3}-3 x^{2}+b x+c$ has a local minimum at -5 and a local maximum at $x=\frac{-1}{2}$ and inflection point at $x=\frac{1}{4}$ find $a, b, c \in R$ .

Q3: A) Let M be a point moving on the curve $y^{2}=x^{3}$ such that rate of change the point $M$ getting away from of the origin point is 4 unit $/ \mathrm{s}$ . Find the rate of chang of the x -coordinate for M when $x=2$

$\lim _{x \rightarrow 0^{+}} x-1-\frac{2 \ln x^{2}}{\sqrt{x}}$

$\int_{0}^{1} \int_{0}^{y^{2}} \sqrt{1+y^{3}} d x d y$