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# Calculus Questions - All Grades

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Evaluate the limit. $lim_{x->5} (x^2 - 2x - 15)/(x^2 - 25)$
1. $0$
2. $4/5$
3. $1$
4. $1/2$
College Integrals
Find the following indefinite integral
$int(8x^8 -6) dx$
1. $8/9x^9+C$
2. $64x^7+C$
3. $8/9x^9-6x+C$
4. $8/9x^9-6+C$
What is the second derivative of $f(x)=3x^3+2x^2$?
1. $f''(x)=18x+4$
2. $f''(x)=9x^2+4x$
3. $f''(x)=18$
4. $f''(x)=0$
Find the average rate of change of $f(x)=-4x^2+3x-4$ on the interval $[-1, 3]$.
1. $-1/5$
2. $5$
3. $1/5$
4. $-5$
College Integrals
Find the following indefinite integral:
$int(-7x^2+ 4/x- 5/x^4) dx$
1. $-7x^3 + 4 ln(|x|) -5x^-3 +C$
2. $1/3x^3 + 4ln (|x|) + 5/3 x^-3 +C$
3. $-7/3x^3 + 4ln(|x|) + 5/3x^-3 +C$
4. $-14x - 4x^-2 + 20x^-5 +C$
On what intervals is the function $f(x)=3x^3+2x^2$ increasing or decreasing?
1. Increasing: $(-oo,-4/9) uu (0, oo)$, decreasing: $(-4/9, 0)$
2. Increasing: $(-oo,-4/9)$, decreasing: $(-4/9, 0)$
3. Increasing: $(-oo,0) uu (-4/9, oo)$, decreasing: $(-4/9, 0)$
4. Increasing: $(-4/9, 0)$, decreasing: $(-oo,-4/9) uu (0, oo)$
Describe the end behavior of $f(x)=2^x-3$.
1. $"As " x -> -oo, y-> -3; \ "as " x->oo, y->oo$
2. $"As " x -> -oo, y-> oo; \ "as " x->oo, y->oo$
3. $"As " x -> -3 , y-> oo; \ "as " x->oo, y->oo$
4. $"As " x -> -oo, y-> oo; \ "as " x->oo, y->-3$
On $f(x)=2x^5+x^3-3x$
1. $(-0.65,1.4)$ is a relative and absolute maximum.
2. $(0.65,-1.4)$ is a relative and absolute minimum.
3. $(-0.65,1.4)$ is a relative maximum.
4. $(0.65,-1.4)$ is a relative minimum.
5. Both A and B.
6. Both C and D.
7. None of the above.
Identify the intervals on which the given function is increasing and decreasing.
$f(x)=x^3+x^2-x$
1. Increasing: $(-oo, -1) uu (1/3,oo)$; decreasing: $(-1, 1/3)$
2. Increasing: $(-oo, -1)$; decreasing: $(-1, 1/3)$
3. Increasing for all x
4. Increasing: $(-1,1/3)$; decreasing: $(-oo, -1) uu (1/3,oo)$
What is the derivative of $f(x)=3x^3+2x^2$?
1. $f'(x)=9x^2+4x$
2. $f'(x)=3x^2+2x$
3. $f'(x)=0$
4. $f'(x)=12x^2+6x$