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# Calculus Questions - All Grades

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Evaluate the limit. $lim_{x->9} (x-9)/(sqrt(x)-3)$
1. Indeterminate
2. $0$
3. $3$
4. $6$
Find the derivative. $f(x) = root[5](x^7)$
1. $f'(x) = root[5](7x^6)$
2. $f'(x) = 7/5 root[5](x^2)$
3. $f'(x) = root[4](x^6)$
4. $f'(x) = root[5](x^2)$
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. $"As " x -> -oo, y-> oo; \ "as " x->oo, y->-3$
What is the limit of $f(x)=3x^3+2x^2$ as $x$ approaches 5?
1. $lim_(x->5)f(x)=425$
2. $lim_(x->5)f(x)=452$
3. $lim_(x->5)f(x)=542$
4. $lim_(x->5)f(x)=245$
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. $f'(x)=12x^2+6x$
Differentiate. $f(x) = (4x^100)/25$
1. $f'(x) = (4x^99)/25$
2. $f'(x) = (8x^10) / 5$
3. $f'(x) = x^99 / 625$
4. $f'(x) = 16x^99$
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.
Find the derivative. $f(x) = 2x^0.4 - 8x^(-0.02)$
1. $f'(x) = 2x^(-0.4) - 8x^(-1.02)$
2. $f'(x) = 0.8x^(-0.6) + 0.16x^(-1.02)$
3. $f'(x) = 2 + 0.16x^(-1.02)$
4. $f'(x) = 0.5x^(-0.6) + 0.4 x^(-1.02)$
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: $(-oo,-4/9) uu (0, oo)$
Evaluate the limit. $lim_{x->0} ((x-5)^2-25)/x$
1. Does not Exist
2. $-10$
3. $oo$
4. $0$
What are all the values of $x$ for which the function $f$ defined by $f(x)=x^3+3x^2-9x+7$ is increasing?
1. $-3< x<1$
2. $-1< x< 1$
3. $x<-3$ and $x>1$
4. $x<-1$ and $x>3$
5. All real numbers
Find the intervals of increase and decrease for the following function. $f(x) = sqrt(3x^2 - 9x + 6)$
1. Increasing on $(3/2,oo)$ and decreasing on $(-oo, 3/2)$
2. Increasing on $(2,oo)$ and decreasing on $(-oo,1)$
3. Increasing on $(3/2,oo)$
4. Increasing on $(2,oo)$
$f(x)=x^2 e^(-x^2)$
1. Increasing: $(-oo, -1) uu (0,1)$; decreasing: $(-1, 0) uu (1,oo)$
2. Increasing: $(-oo, 0)$; decreasing: $(0, oo)$
4. Increasing: $(-1,0) uu (1,oo)$; decreasing: $(-oo, -1) uu (0,1)$