Math Statement

Problem 26901

Calculate $6,135 \times 5$ .

See Solution

Problem 26902

Find the limit as $x$ approaches 0 for the expression $x^{4}-\frac{4^{x}}{8000}$ .

See Solution

Problem 26903

Simplify $2\left(a^{2} b^{-1}\right)$ and express with positive exponents.

See Solution

Problem 26904

Solve the equation $3=-2\left|\frac{1}{4} s-5\right|+3$ .

See Solution

Problem 26905

Simplify the expression $\left(\frac{-2 m}{n}\right)^{2}$ using exponent properties and show only positive exponents.

See Solution

Problem 26906

Simplify the expression $\left(\frac{y}{x}\right)^{9}$ using exponent properties, showing only positive exponents.

See Solution

Problem 26907

Score Part III Find the $\frac{d y}{d x}$ . ( 4 scores per question. The total is 12 scores.)
12. $y=x \sin x$ .
13. $y=\frac{x^{2}-1}{x^{2}+1}$ .

See Solution

Problem 26908

Score Part IV Find the $d y$ . ( 5 scores per question. The total is 10 scores.)
15. $y=\sin (\tan x+\cos x)$ .
16. $e^{y}-x^{2} y=0$ .

See Solution

Problem 26909

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

See Solution

Problem 26910

21. Consider the function $f(x)=\frac{x^{3}-4 x}{x^{3}+1}$ . (1) Find the domain, the $x$ - and $y$ -intercepts, (2) Find the asymptotes, (3) Find the intervals of increase and decrease. (Tip: The root for $8 x^{3}+3 x^{2}-4=0$ is $x \approx 0.68636$ .)

See Solution

Problem 26911

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

See Solution

Problem 26912

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

See Solution

Problem 26913

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

See Solution

Problem 26914

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

See Solution

Problem 26915

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

See Solution

Problem 26916

\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. $\int_{1}^{2}\left(x^{3}\right) d x$ .

See Solution

Problem 26917

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

See Solution

Problem 26918

If $x=5 y$ , then $x \propto$

See Solution

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Math Statement

Problem 26901

Calculate $6,135 \times 5$ .

Problem 26902

Find the limit as $x$ approaches 0 for the expression $x^{4}-\frac{4^{x}}{8000}$ .

Problem 26903

Simplify $2\left(a^{2} b^{-1}\right)$ and express with positive exponents.

Problem 26904

Solve the equation $3=-2\left|\frac{1}{4} s-5\right|+3$ .

Problem 26905

Simplify the expression $\left(\frac{-2 m}{n}\right)^{2}$ using exponent properties and show only positive exponents.

Problem 26906

Simplify the expression $\left(\frac{y}{x}\right)^{9}$ using exponent properties, showing only positive exponents.

Problem 26907

Score Part III Find the $\frac{d y}{d x}$ . ( 4 scores per question. The total is 12 scores.)
12. $y=x \sin x$ .
13. $y=\frac{x^{2}-1}{x^{2}+1}$ .

Problem 26908

Score Part IV Find the $d y$ . ( 5 scores per question. The total is 10 scores.)
15. $y=\sin (\tan x+\cos x)$ .
16. $e^{y}-x^{2} y=0$ .

Problem 26909

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

Problem 26910

21. Consider the function $f(x)=\frac{x^{3}-4 x}{x^{3}+1}$ . (1) Find the domain, the $x$ - and $y$ -intercepts, (2) Find the asymptotes, (3) Find the intervals of increase and decrease. (Tip: The root for $8 x^{3}+3 x^{2}-4=0$ is $x \approx 0.68636$ .)

Problem 26911

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

Problem 26912

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

Problem 26913

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

Problem 26914

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

Problem 26915

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

Problem 26916

\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. $\int_{1}^{2}\left(x^{3}\right) d x$ .

Problem 26917

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

Problem 26918

If $x=5 y$ , then $x \propto$

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Math Statement

Problem 26901

Calculate 6,135×56,135 \times 56,135×5.

Problem 26902

Find the limit as xxx approaches 0 for the expression x4−4x8000x^{4}-\frac{4^{x}}{8000}x4−80004x​.

Problem 26903

Simplify 2(a2b−1)2\left(a^{2} b^{-1}\right)2(a2b−1) and express with positive exponents.

Problem 26904

Solve the equation 3=−2∣14s−5∣+33=-2\left|\frac{1}{4} s-5\right|+33=−2∣∣​41​s−5∣∣​+3.

Problem 26905

Simplify the expression (−2mn)2\left(\frac{-2 m}{n}\right)^{2}(n−2m​)2 using exponent properties and show only positive exponents.

Problem 26906

Simplify the expression (yx)9\left(\frac{y}{x}\right)^{9}(xy​)9 using exponent properties, showing only positive exponents.

Problem 26907

Score Part III Find the dydx\frac{d y}{d x}dxdy​. ( 4 scores per question. The total is 12 scores.)12. y=xsin⁡xy=x \sin xy=xsinx.13. y=x2−1x2+1y=\frac{x^{2}-1}{x^{2}+1}y=x2+1x2−1​.

Problem 26908

Score Part IV Find the dyd ydy. ( 5 scores per question. The total is 10 scores.)15. y=sin⁡(tan⁡x+cos⁡x)y=\sin (\tan x+\cos x)y=sin(tanx+cosx).16. ey−x2y=0e^{y}-x^{2} y=0ey−x2y=0.

Problem 26909

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

Problem 26910

Problem 26911

22. Consider f(x)=x2−3x+3f(x)=x^{2}-3 x+3f(x)=x2−3x+3 and g(x)=xg(x)=xg(x)=x. (1) Find the points of intersection, (2) Find the area of the region between two curves.

Problem 26912

Score Part III Find the dydx\frac{d y}{d x}dxdy​. (4 scores per question. The total is 12 scores.) 12. y=xsin⁡xy=x \sin xy=xsinx.13. y=x2−1x2+1y=\frac{x^{2}-1}{x^{2}+1}y=x2+1x2−1​.14. y=ln⁡(2x3+1)y=\ln \left(2 x^{3}+1\right)y=ln(2x3+1).

Problem 26913

16. ey−x2y=0e^{y}-x^{2} y=0ey−x2y=0.

Problem 26914

16. ey−x2y=0e^{y}-x^{2} y=0ey−x2y=0.

Problem 26915

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

Problem 26916

\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∫12​(x3)dx.

Problem 26917

ScorePart 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 tf(x)=∫2xx2​tetdt, find f′(x)f^{\prime}(x)f′(x).

Problem 26918

If x=5yx=5 yx=5y, then x∝x \proptox∝

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Calculate $6,135 \times 5$ .

Find the limit as $x$ approaches 0 for the expression $x^{4}-\frac{4^{x}}{8000}$ .

Simplify $2\left(a^{2} b^{-1}\right)$ and express with positive exponents.

Solve the equation $3=-2\left|\frac{1}{4} s-5\right|+3$ .

Simplify the expression $\left(\frac{-2 m}{n}\right)^{2}$ using exponent properties and show only positive exponents.

Simplify the expression $\left(\frac{y}{x}\right)^{9}$ using exponent properties, showing only positive exponents.

Score Part III Find the $\frac{d y}{d x}$ . ( 4 scores per question. The total is 12 scores.)
12. $y=x \sin x$ .
13. $y=\frac{x^{2}-1}{x^{2}+1}$ .

Score Part IV Find the $d y$ . ( 5 scores per question. The total is 10 scores.)
15. $y=\sin (\tan x+\cos x)$ .
16. $e^{y}-x^{2} y=0$ .

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

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

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

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

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

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

\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. $\int_{1}^{2}\left(x^{3}\right) d x$ .

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

If $x=5 y$ , then $x \propto$