How to write equations

Practice Questions

CLEP Calculus › How to write equations

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1

Take the indefinite integral of

$\int x(x^6+7)^2dx$

2

What is the equation of the tangent line at x = 15 for f(x) = x4 + 5x2 + 44x – 3?

3

Given the one-to-one equation f(x)=3x+1, the inverse function f-1(y)=

4

You wish to find the area under the line between the values of and . Which is the correct way to express this task as an equation?

5

Find the implicit derivative $\frac{\mathrm{d} y}{\mathrm{d} x}$ of at the point .

6

Find the limit:

${} \lim_{x\rightarrow \infty} \frac{3x^2+5x+2}{2x^2+x+1}$

7

Find the limit of $lim_{x \to 0}\frac{sin(2x)}{x}$ .

8

Find the equation tangent to $y=x\sin x$ at $x=\pi$

9

Determine given that $f'(x) = 12x^{3}+12x^{2}+12x+12$ .

10

Give the position equation for an object falling towards Earth with a constant acceleration of $-9.8 \frac{m}{s^2}$ , with initial velocity of $13 \frac{m}{s}$ , and initial position at above the ground.

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