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# Calculus Questions - All Grades

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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. $8/9x^9-6+C$
College Integrals
Find the following indefinite integral.
$int(-3/x+2x^(-1/4) - 8e^x) dx$
1. $-ln(|x|) -8/3x^(3/4)-8e^x +C$
2. $-1/3ln(|x|) + 8/3x^(3/4) - 8e^x+C$
3. $-3 ln(|x|) + 8/3x^(3/4)-8e^x +C$
4. $-3 ln(|x|) + 8/3x^(3/4) - 8/xe^x+C$
Find the value of the integral $int_0^1e^x/(e^x+1)dx$.
1. $ln((e+1)/2)$
2. $(e-1)/2$
3. $ln(e-1)$
4. $e+1$
Find the value of the integral $int_1^e1/xdx$.
1. $-1$
2. $e$
3. $1/2$
4. $1$
Find the value of the integral $int_1^2(x^2+1)/xdx$.
1. $1/2ln2$
2. $1+ln2$
3. $3/2+ln2$
4. $3/2-ln2$
Find the value of $int_0^(ln2)3e^(4x)dx$.
1. $41/4$
2. $45/4$
3. $43/4$
4. $21/2$
Find the value of the integral $int_(-e^2)^(-e)3/xdx$.
1. $-3$
2. $-e$
3. $e^3$
4. $1/3$
On what intervals is the function $f(x)=3x^3+2x^2$ concave upwards and downwards?
1. concave upward $(-2/9, oo)$, concave downward $(-oo, -2/9)$
2. concave upward $(-oo, -2/9)$, concave downward $(-2/9, oo)$
3. concave upward $(0, oo)$, concave downward $(-oo, 0)$
4. concave upward $(-oo, 0)$, concave downward $(0, oo)$
Evaluate the limit. $lim_{x->5} (x^2 - 2x - 15)/(x^2 - 25)$
1. $0$
2. $4/5$
3. $1$
4. $1/2$
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. $f''(x)=0$
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. $-14x - 4x^-2 + 20x^-5 +C$
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: $(-oo, -1) uu (1/3,oo)$
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. $-5$
Evaluate the limit. $lim_{x->9} (x-9)/(sqrt(x)-3)$
2. $0$
3. $3$
4. $6$