MAT 1300 Study Guide - Final Guide: Antiderivative, Marginal Cost

df dx 1. Find if f(x)=x ex-ex In(t) dt Y 3. Find dy if y = sin(x3 + 1) 4. Find the absolute maximum and minimum values of the function f(x) x3 - 3x2 +1 on [-1/2, 4].

Show by explicit computation that S(2ex) 2s(ex). Is S linear? For the transformation S in part(c),find two functions f and g, f g, such that S(f+g) S(f) + S(f). Let U be defined by U(f) = 1 -1 xf(x)dx Is U linear? Let C([-1,1]) be the vector space of continuous functions on the interval [-1,1] and define T: C ([-1,1]) rightarrow R by T(f) = 1 -1 f(x) dx Thus, for example, T(x3) = 1 -1 x3 dx = x4/4 1 -1 = 0 Let f(x) = ex and g(x) = x2 for -1

Quix 9 Math 1300 Section 004 Calculus I Name: Seore 1. Find the gemeral antiderivative of the following functions (3 points) x)+a b) (3 points) le) 1 +6 (c) (3 points)玔t) = tan(t) cos(f) 2. (3 points) Find the antiderivative of g(r)- +" passing through the (