MAT 126 Midterm: F14mt1sol

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turquoisegnu128

31 Jan 2019

School

University of Maine

Department

Mathematics and Statistics

Course

MAT 126

Professor

All

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October 1, 2014: (10 pts) let h(x) be the function whose graph is shown below. Find the following values, if they exist: (a) lim x 2 (b) lim x 4 h(x) = 3 h(x) = 1: (10 pts) evaluate the following limits. (a) lim x 1 (b) lim x 1 sin( . = lim x 1 (x 1) ( x 1) ( x + 1) ( x + 1) 2 ). (x 1)( x + 1) (x 1) ( x + 1) = 2. = lim x 1: (26 pts) shown is the graph of the equation y = x3 + x ex (a) (14 pts) find the derivative dy dx. ex(3x2 + 1) (x3 + x)ex. By the quotient rule, dy dx (ex)2 (b) (12 pts) sketch the tangent line at the point (0, 0) on the above graph, and nd an equation for it.

Related Questions

1. (25 pts) The graph of a function fis given in the figure below. The domain of fis (-, +.). Use the graph of fto answer the questions below. y = f(x) y=f(x) -3 -1 1 2 3 4 (I) (1 pt) Find the range of f. Range of f = (II) Find the following values. (Note: Possible answers include + , -, or "does not exist".) (a) (1 pt) lim f (x) = x+3+ (b) (1 pt) lim f (x) = (C) (1 pt) lim f (x) = x+3 (a) (1 pt) f(3) = (e) (2 pts) lim f (x) = (f) (2 pts) lim f(x) = (g) (2 pts) lim f (x) = (h) (2 pts) lim f (x) = (i) (2 pts) lim f (x) = (III) (2 pts) Find all vertical asymptotes. (IV) (2 pts) Find all horizontal asymptotes. (V) (2 pts) Find all slant asymptotes. (VI) (4 pts) Determine the intervals of continuity for f.

1. (32 pts) The graph of a function f is given in the figure below. The domain of fis (-0, +). Use the graph of fto answer the questions below. y = f(x) y=f(x) (I) (2 pts) Find the range of f. Range of f = (II) Find the following values. (Note: Possible answers include + co, -, or "does not exist".) (a) (2 pts) lim f (x) = X+1 + (b) (2 pts) lim f (x) = (c) (2 pts) lim f (x) = x+1 (a) (2 pts) f(1) = (e) (2 pts) lim f (x) = (f) (2 pts) lim f (x) = (g) (2 pts) lim f (x) = (h) (2 pts) lim f (x) = (i) (2 pts) lim f (x) = (j) (2 pts) f (0) = (III) (2 pts) Find all vertical asymptotes. (IV) (2 pts) Find all horizontal asymptotes. (V) (2 pts) Find all slant asymptotes. (VI) (4 pts) Determine the intervals of continuity for f.

4. (26 pts) Evaluate the limit or say that the limit does not exist . If a limit does not exist, explain why. Show your work. You may NOT use a table of values, a graph, or L' Hospitals's Rule to justify your answer. (Note: Possible answers include + or -.) X-2 (a) (10 pts) lim – x+2 782 +5 - 3 (b) (8 pts) xvot COS X OSCILLATES lim x → x + 4 x2 Since -1 scos x si, we have that -1 (c) (8 pts) cos x x + 4 x2 1 x + 4 x? x + 4 x2 -1 1 and since lim – Elim- x+ x + 4 x2 + x + 4 x2 * +422=0, it follows by the Squeeze Theorem that lim Co2 = 0. X +0 x + 4 x 2

MAT 126 Midterm: F14mt1sol

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