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Problem 30701

Part IV Find the dyd y. ( 5 scores per question. The total is 10 scores.)
15. y=sin(tanx+cosx)y=\sin (\tan x+\cos x).

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Problem 30702

22. Consider f(x)=x23x+3f(x)=x^{2}-3 x+3 and g(x)=xg(x)=x. (1) Find the points of intersection, (2) Find the area of the region between two curves.

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Problem 30703

Score Part III Find the dydx\frac{d y}{d x}. (4 scores per question. The total is 12 scores.) 12. y=xsinxy=x \sin x.
13. y=x21x2+1y=\frac{x^{2}-1}{x^{2}+1}.
14. y=ln(2x3+1)y=\ln \left(2 x^{3}+1\right).

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Problem 30704

16. eyx2y=0e^{y}-x^{2} y=0.

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Problem 30705

16. eyx2y=0e^{y}-x^{2} y=0.

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Problem 30706

14. y=ln(2x3+1)y=\ln \left(2 x^{3}+1\right).

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Problem 30707

\begin{tabular}{|l|} \hline Score \\ \hline \\ \hline \end{tabular}
Part V Evaluate the following integral. (5 scores per question. The total is 10 scores.)
17. 12(x3)dx\int_{1}^{2}\left(x^{3}\right) d x.

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Problem 30708

Score Part VI Solve the following questions. (4 scores per question. The total is 8 scores.)
19. Consider y=13x3x+1y=\frac{1}{3} x^{3}-x+1 on the interval [0,3][0,3], find the absolute maximum and minimum values of y .

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Problem 30709

\begin{tabular}{|l|} \hline Score \\ \hline \end{tabular}
Part V Evaluate the following integral. (5 scores per question. The total is 10 scores.)
18. 11(e2x12+x)dx\int_{-1}^{1}\left(e^{2 x}-\frac{1}{2+x}\right) d x.

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Problem 30710

Score
Part VI Solve the following questions. (4 scores per question. The total is 8 scores.)
20. Consider f(x)=2xx2tetdtf(x)=\int_{2 x}^{x^{2}} t e^{t} d t, find f(x)f^{\prime}(x).

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Problem 30711

If x=5yx=5 y, then xx \propto

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Problem 30712

Find the volume and Surface Area 380.

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Problem 30713

```latex احسب النهايات للدالة f(x)=xx+ex f(x) = \frac{x}{x + e^{-x}} عندما يقترب x x من المالانهاية و من الصفر.

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Problem 30714

EXERCICE 1: le plan est rapporté a un repère orthonormé (o;i;j).
1. Donner une représentation paramétrique de la droite (D)(D) passant par le point A(2;1)A(2 ;-1) et de vecteur directeur u(2;1)\vec{u}(2 ; 1).
2. Donner une équation cartésienne de la droite (Δ)(\Delta) passant par le point B(1;1)B(-1 ; 1) et de vecteur directeur vˉ(1;3)\bar{v}(1 ; 3).
3. Soit (D)\left(D^{\prime}\right) la droite définie par sa représentation paramétrique (D):{x=2ty=2+2t,(tR)\left(D^{\prime}\right):\left\{\begin{array}{l}x=2-t \\ y=2+2 t\end{array},(t \in \mathbb{R})\right., et ( Δ)\left.\Delta^{\prime}\right) la droite définie par l'équation cartésienne (Δ):xy3=0\left(\Delta^{\prime}\right): x-y-3=0. a- le point E(1;4)E(1 ; 4) est-il un point de la droite (D)\left(D^{\prime}\right) ? b-monter que (D)\left(D^{\prime}\right) et ( Δ)\left.\Delta^{\prime}\right) sont sécantes. c-déterminer les coordonnées du point I, point d'intersection de ( DD^{\prime} ) et ( Δ\Delta^{\prime} ).
4. a-déterminer une équation cartésienne de la droite (D1)\left(D_{1}\right) qui passe par le point A(2;3)A^{\prime}(2 ; 3) et parallèle à la droite ( Δ\Delta^{\prime} ). b-déterminer une équation cartésienne de la droite (Δ1)\left(\Delta_{1}\right) qui passe par le point A(2;3)A^{\prime}(2 ; 3) et parallèle à l'axe des abscisses.
5. Construire dans le repère (0,i,j)(0, \vec{i}, \vec{j}) les droites (D),(Δ)\left(D^{\prime}\right),\left(\Delta^{\prime}\right) et (Δ1)\left(\Delta_{1}\right).

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Problem 30715

2. In an experiment to determine the water hardness of tap water, a researcher measured three 50 mL aliquots of water samples and to each sample he added 10 mL of pH 10 ammonia/ammonium chloride buffer and two drops of eriochrome black T indicator and the colour changed to wine red. The resulting solutions were then separately titrated against 0.05 M sodium-EDTA solution from the burette until a final endpoint colour change. The data obtained was recorded in a table as shown below. \begin{tabular}{|l|l|l|l|} \hline Titration & 1 & 2 & 3 \\ \hline final reading /mL/ \mathrm{mL} & 10.70 & 10.65 & 10.60 \\ \hline Initial reading /mL/ \mathrm{mL} & 0.00 & 0.00 & 0.00 \\ \hline Titre value /mL/ \mathrm{mL} & & & \\ \hline \end{tabular} a) What is the expected endpoint colour change? b) Calculate the average titre of the results? c) Write a balance equation of reaction between calcium ions and EDTA d) Calculate the number of moles of EDTA used in each titration and the average number of moles for the whole process. e) What is the concentration of Ca2+\mathrm{Ca}^{2+} (expressed as ppmCaCO3\mathrm{ppm} \mathrm{CaCO}_{3} ) in the sample?

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Problem 30716

An aircraft is climbing at a 30 degree angle to the horizontal. How fast is the aircraft gaining altitude if its speed is 500mi/hr500 \mathrm{mi} / \mathrm{hr} ? Express your answer as mi/hr\mathrm{mi} / \mathrm{hr} and round it into the nearest whole number. Input only the numerical value of the answer without the unit.

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Problem 30717

(4) What is the sum of 60 numbers 80 and 80 numbers 60 ? of the. 48 C 60 B 84 One thousand \%\%

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Problem 30718

3075750\begin{array}{r}-30 \\ 75 \\ -75 \\ \hline 0\end{array}

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Problem 30719

Which statement describes how the graph of a function, h(x)h(x), and its inverse, h1(x)h^{-1}(x), are related? The line y=xy=-x is the perpendicular bisector of each segment connecting a point on h(x)h(x) to the corresponding point on h1(x)h^{-1}(x). The line y=xy=x is the perpendicular bisector of each segment connecting a point on h(x)h(x) to the corresponding point on h1(x)h^{-1}(x). The graph of the inverse of h(x)h(x) is a reflection over the line y=0y=0 of the graph of h(x)h(x). The yy-axis is the perpendicular bisector of each segment connecting a point on h(x)h(x) to the corresponding point on h1(x)h^{-1}(x).

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