CALCULUS ll'llll'lA Homework Assignment #4 Due: Dec 7th at 11:59pm {EST} on gradescopema For full credit. ensure you sho'ar all your work and explain your reasoning. Simply stating the nal answer for any of the following questions will not result in full credit. You should avoid using calculators and leave your answers in exact form. even in questions involving words like \"approximately" you won't increase your grade by showing us the decimal expansion of your results. so don't worry about that extra step. Make sure you read and follo'itr the submission instructions for lGradescope. 1. {3 marks} Suppose that 9"{3} = 2 r sinl[:r:} and that g'{} = :l and gm} = 1. Find gfz} and explain your reasoning. E'. {a} {2 marks} Evaluate the Riemann sum for ne} = 412 3. taking the sample points to be right endpoints and n. = I]. b = 4 and n = 4. {b} {1 mark} Evaluate .1 f {-1.122 Md: El by using a similar scheme as in part {a} but taking the limit as n :> 00. 3. {3 marks} If f and g are continuous functions with [1 snags: =ss -l and a j g{.r}dz = 21. 1 find .1. 1 {ago} you] v\"?! {1 1}'2]d$- 1 4. {3 marks} Suppose that a function f is dened by as = fie\"tbs. Determine the intervals on which I is concave 11p and concave dos-n. o. {3 marks} Evaluate {3 + Insists: mend: [ 4.: ' 2 . [3 marks} Determine the area of the region bounded by y = I :r: [i and y = 230 + -'1