can you please help me solve these questions!

50% X . . . 8:57 PM Tue Nov 2 Untitled (Draft) ~ Q n Untitled (Draft) X 1.1+Introduction+to+Limits X X Lecture+Notes+-+Chem+4311-+Fall+2021 O CO A 1. Find the slope of the line tangent to the graph of f (x) = " at x = 2. 7. Assume f is a differentiable function whose graph passes through the point (1,3). Suppose g(x) = f(x2) and the line tangent to the graph of f at (1,3) is y = 5x - 2. [A] e2 * e [D] [E] 92 Find g'(1). [A] 7 [B] 10 6 [D] 3 [E] 8 2. Find the value of x for which the slope of the line tangent to the graph of f(x) = 2xe5x is 0. [A] 0 [B] - 2 [D] 1 [E] - . Find a value of the constant c that will make f (x) continuous at x = 0. sin(5x) if x #0 f(x) =3 if x = 0 MATH 1426 Exam #2 - Version A Fall 2021 [A] 0 [B] - [C] - [D] 8. Given y = sin?(e 3x+1), find y' [A] -6 sin(e 3x+1) [B] 6x sin(e 3x+1) cos(e 3x+1) 4. Suppose the position of an object moving horizontally after t seconds is given by [C] 6e 3x+1 sin(e 3x+1) cos(e 3x+1) g(t) = 10t - 2t3 for t > 0, where g is measured in feet. Find the acceleration of the [D] -2e 3x+1 sin(e 3x+1) cos(e 3x+1) object when t = 2. Label your answer with appropriate units. [E] 2 sin(e 3x+1) cos(e 3x+1) [A] Oft/s [B] Oft/$2 [C] -24 ft/s [D] -24 ft/$2 [E] 24 ft/s 9. Find the slope of the tangent line to the graph of sin y = 2x4 - 2 at the point (1, It). . [ Same scenario as #4) Suppose the position of an object moving horizontally after t [A] 2 [B] -4 0 [D] -8 [E] undefined seconds is given by g(t) = 10t - 2t' fort > 0, where g is measured in feet. At what moment of time is the velocity of the object -2 feet per second? [A] V2 seconds [B] 1 second [C] V3 seconds 10. Find the derivative of the function y. [D] 2 seconds [E] 3 seconds y = 5. 11* - 2 . 10810(x) [A] (5 In 11) . 11* - [B] (In 11) . 11* + 2In10 [$) (52) . 11* -1 -InTo [D] (In 11) . 11* -10 . The figure shows the graphs of three functions. One is the position of a car, one is the [E] (5 In 11) . 11*-1 + xin 10 velocity of the car, and one is the acceleration. Which does each function represent? 11. If the slope of the curve y = f-1(x) at the point (3,1) is =, find f'(1). [A] 0 [B] 1 [C] 3 [D] - [A] h is position, g is velocity, f is acceleration [B] g is position, f is velocity, h is acceleration [C] f is position, g is velocity, his acceleration D] f is position, h is velocity, g is acceleration [E] g is position, h is velocity, f is acceleration