MAC 2311 Midterm: MAC2311 S10 Test 3

1. (a) Find the linearization of f(x)-V8+x at x-1. (5 pts.) (b) Use (a) to approximate 10. (5 pts.) (c) Sketch the function and its linearization. (5 pts.)

Find the linearization L(x) of the function at a. f(x) = x 1/2, a = 16 L(x) =

t of er = 4-2.2 Correct to six decimal places (6) (12 pts ] (a) Find a function f such that f, (z) = 13 and the line at +yO is tangent to the graph of f (b) F ind a general antiderivative of f(x) = 51:1/, s(x) + -3 sect + 2 co (7) [10 pts] Find the limit (a) lim VV rl 2-2 ) sin(t) (b) lim 3 (8) [10 pts] dy log (t2) dt. Find y(r) (a) y / /9_y2dt. Find y'(0) definition of the integral in terms of the limit of a Riemann sun to (b) x2- tan r 2t2 (9) [8 pts) Use the 4 evaluate 10) [10 pts] Evaluate the integrals (z-2)? 3