Calc BC Exam Questions and Answers
~(3x+1)/(x^2-4x+3)= - ANSWER-5ln[x-3] - 2ln[x-1] + c
∫(x/2)(e^-3x/4) - ANSWER-((-2x/3)e^-3x/4) + ((3/8)e^-3x/4) + c
∫0 5 √((5-x)/5) - ANSWER-10/3
∫1/t√t dt= - ANSWER--2t^(-1/2) + c
A cube with edges of length x centimeters has volume V(x)=x^3 cubic centimeters. The
volume is increasing at a constant rate of 40 cubic centimeters per minute.
At the instant when x=2, what is the rate of change of x, in centimeters per minute, with
respect to time? - ANSWER-10/3
A particle moves in the xy-plane so that its position for t>= is given by the parametric
equations x=ln(t+1) and y=kt^2, where k is a positive constant. The line tangent to the
particle's path at the point where t=3 has slope 8.
What is the value of k? - ANSWER-1/3
If ∫4 -10 g(x)=-3
and ∫4 6 g(x)=5
then ∫-10 6 g(x)= - ANSWER-8
If f(x)= (5-x)/(x^3+2)
f'(x)= - ANSWER-(2x^3-15x^2-2)/(x^3+2)^2
If f(x)= E x^2n/n!
f'(x)= - ANSWER-2x + 2x^3 + x^5 + x^7/3 + ... + 2nx^2n-1/n!
If f(x)=3x^2+2x
f'(x)= - ANSWER-lim as h->0 (3(x+h)^2+2(x+h))-(3x^2+2x) / h
If f(x)=cos^2(3x-5)
f'(x)= - ANSWER--6sin(3x-5)cos(3x-5)
, If g is a twice-differentiable function, where g(1)=0.5 and lim as x->infinite g(x)=4
then ∫1 ∞ g'(x)= - ANSWER-3.5
If the average value of a continuous function f on the interval [-2,4] is 12
what is ∫-2 4 f(x)/8 - ANSWER-9
If the infinite series
S= E (-1)^n+1 (2/n)
is approximated by Pk= E (-1)^n+1 (2/n)
What is the least value of k for which the alternating series error bound guarantees that
[S-Pk}= 3/100 - ANSWER-68
If x^2+xy-3y=3, then at the point (2,1)
dy/dx= - ANSWER-5
Let f be a twice-differentiable function for all real numbers x.
Which of the following additional properties guarantees that f has a relative minimum at
x=c? - ANSWER-f'(c)=0 and f"(c)>0
Let f be the function given by f(x)=2cosx+1.
What is the approximation for f(1.5) found by using the
line tangent to the graph of f at x=π/2? - ANSWER-π-2
Let f be the function with f(0)=1/pi^2, f(2)=1/pi^2, and derivative given by
f'(x)=(x+1)cos(pix).
How many values of x in the open interval (0,2) satisfy the condition of the MVT for the
function f on the closed interval [0,2]? - ANSWER-two
Let H(x) be an antiderivative of
x^3+sinx / x^2+2
If H(5)=π
H(2)= - ANSWER--5.867
~(3x+1)/(x^2-4x+3)= - ANSWER-5ln[x-3] - 2ln[x-1] + c
∫(x/2)(e^-3x/4) - ANSWER-((-2x/3)e^-3x/4) + ((3/8)e^-3x/4) + c
∫0 5 √((5-x)/5) - ANSWER-10/3
∫1/t√t dt= - ANSWER--2t^(-1/2) + c
A cube with edges of length x centimeters has volume V(x)=x^3 cubic centimeters. The
volume is increasing at a constant rate of 40 cubic centimeters per minute.
At the instant when x=2, what is the rate of change of x, in centimeters per minute, with
respect to time? - ANSWER-10/3
A particle moves in the xy-plane so that its position for t>= is given by the parametric
equations x=ln(t+1) and y=kt^2, where k is a positive constant. The line tangent to the
particle's path at the point where t=3 has slope 8.
What is the value of k? - ANSWER-1/3
If ∫4 -10 g(x)=-3
and ∫4 6 g(x)=5
then ∫-10 6 g(x)= - ANSWER-8
If f(x)= (5-x)/(x^3+2)
f'(x)= - ANSWER-(2x^3-15x^2-2)/(x^3+2)^2
If f(x)= E x^2n/n!
f'(x)= - ANSWER-2x + 2x^3 + x^5 + x^7/3 + ... + 2nx^2n-1/n!
If f(x)=3x^2+2x
f'(x)= - ANSWER-lim as h->0 (3(x+h)^2+2(x+h))-(3x^2+2x) / h
If f(x)=cos^2(3x-5)
f'(x)= - ANSWER--6sin(3x-5)cos(3x-5)
, If g is a twice-differentiable function, where g(1)=0.5 and lim as x->infinite g(x)=4
then ∫1 ∞ g'(x)= - ANSWER-3.5
If the average value of a continuous function f on the interval [-2,4] is 12
what is ∫-2 4 f(x)/8 - ANSWER-9
If the infinite series
S= E (-1)^n+1 (2/n)
is approximated by Pk= E (-1)^n+1 (2/n)
What is the least value of k for which the alternating series error bound guarantees that
[S-Pk}= 3/100 - ANSWER-68
If x^2+xy-3y=3, then at the point (2,1)
dy/dx= - ANSWER-5
Let f be a twice-differentiable function for all real numbers x.
Which of the following additional properties guarantees that f has a relative minimum at
x=c? - ANSWER-f'(c)=0 and f"(c)>0
Let f be the function given by f(x)=2cosx+1.
What is the approximation for f(1.5) found by using the
line tangent to the graph of f at x=π/2? - ANSWER-π-2
Let f be the function with f(0)=1/pi^2, f(2)=1/pi^2, and derivative given by
f'(x)=(x+1)cos(pix).
How many values of x in the open interval (0,2) satisfy the condition of the MVT for the
function f on the closed interval [0,2]? - ANSWER-two
Let H(x) be an antiderivative of
x^3+sinx / x^2+2
If H(5)=π
H(2)= - ANSWER--5.867
