Q3 ( Use the Comparison Theorem to determine if the following integrals converge or diverge. You do {\bf not} have to evaluate the integral if it converges. (a) +1 [." ( 2 ² + 1 ) d dx - e-x (b) 5) /.* (1000)) d dx 3 In(x) 8

Suppose we want to approximate the integral widths. Answer: 10 Write out this sum, using function notation for each term. b(x)da by using a left-hand sum with 4 rectangles of equal Now, approximate the integral b(a)da by using a right-hand sum with 3 rectangles of equal widths. Answer: Write out this sum, using function notation for each term.

Which function grows faster as x → +∞ ? 3x¹ + 2x³ + 3x² +1 3 x³ In(x² + 1)

Consider the function f(x)=x2+6(5x−10)(x+4)f(x)=x2+6(5x-10)(x+4). For each prompt below, if no solution exists - enter "DNE". If there is more than one solution, enter your answer as a comma-separated list (like "1, 3"). You may find it helpful to rewrite the numerator or denominator in a different form to help you complete some of the parts. Determine the vertical intercept of ff. f(0)=f(0)=    Determine the zeros (or "roots") of ff. x=x=    Determine the vertical asymptote(s) of ff. x=x=    Determine the horizontal asymptote of ff. y=y=