Can someone check my answers:
1) Use geometry to evaluate 6 int 2 (x) dx where f(x) = { |x|, -2 <= x <= 2}
{2, 2 < x <= 4}
{-x+4 4 < x <= 6}
for my answer I got 0.512
2) The base of a solid is bounded by y = √x+2, the x-axis and the line x = 1. The cross sections, taken perpendicular to the x-axis, are squares. Find the volume of the solid.
a) 0.5
b) 3.464 <-- my answer
c) 4.5
d) None of the above
3) The function f is continuous on the interval [4,15], with some of its values given in the table. Estimate the average value of the function using trapezoidal approximation.
x: 4 9 11 14 15
f(x): -6 -11 -18 -21 -25
a) -12.727
b) -11.546 <-- my answer
c) -16.273
d) -13.909
4) If the graph of f"(x) is continuous and has a relative maximum of x = c, which of the following can be true"
a) The graph of f has an x-intercept of x = c
b) The graph of f has an inflection point at x = c
c) The graph of x has a relative maximum at x = c <-- my answer
d) None of the above is necessarily true
5) Which of the following shows that g(x) grows faster than f(x)?
a) lim x--> inf f(x)/g(x) = 1000 <-- my answer
b) lim x --> inf f(x)/g(x) = 0
c) lim x--> inf f(x)/g(x) = inf
d) None of these
6) Find F'(x) for F(x) = 2intx^3 sin(t^4) dt
a) sin(2^4) - sin(x^12)
b) sin(x^7)
c) -sin(x^12) <-- my answer
d) -3x^2sin(x^12)
Thank you!
check your first posting
https://www.jiskha.com/display.cgi?id=1531716564