MAT 1800 Midterm: MAT1800 Wayne State 1800 W18

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turquoisegnu128

15 Feb 2019

School

Wayne State University

Department

Mathematics

Course

MAT 1800

Professor

All

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Document Summary

All work must be shown in the provided. Point values appear at the beginning of each problem and total 200. Only minimal credit will be awarded for answers without supporting work. Do not use a calculator: (6 pts each) let xf x. Find and simplify each of the following. (a) X (b: (10 pts) sketch a graph of the function xf. 1: (12 pts) find the domain of the function xf. X: (14 pts) find the average rate of change of the function xg x. 3 x from ax to hax and simplify your answer so that no single factor of h is left in the denominator: (12 points) given that x. Xp of: (6 pts each) a rectangular box has a height of 2 feet. , labeling all intercepts and asymptotes: (12 pts) solve the logarithmic equation. 3: (8 pts each) find the exact value of each expression. (a) log16. 5: (12 pts) the general function tp.

Related Questions

Help with 34,28,40 please (all parts )

4. (21 pts) Let g be the function given by ( 6 - X 2 + x if x < 2, x + -2 g(x) = x2 – x-1 if x>2. (a) (6 pts) Use the definition of continuity to determine whether the function g is continuous at 2. Show your work. (b) (3 pts) Evaluate the limit. Justify your answer. Show your work. Write "does not exist" only if the limit does not exist and is not + or -0. lim g(x) = lim -2+ = +00 X 2 + X since the form of the limit is NUM: POS, DENOM: POS (c) (2 pts) Write the equation(s) of all vertical asymptotes of g. Write "none" if appropriate. The result in part (b) implies that the line x= -2 is a vertical asymptote. This is the only vertical asymptote, since the function g is continuous on its domain (d) (2 pts) Determine the largest) intervals of continuity of g. Use interval notation to write your answer. Let g be the function given by 12+ if x < 2, x# -2 2 + x g(x)= x2-x-1 x-1 if x>2. (e) (6 pts) Evaluate each limit. Do not use L'Hôpital's Rule. Write "does not exist" only if the limit does not exist and is not too or -00. Show your work. 6-1 i lim g(x) = lim -00 2 + X = lim -002 + x 0-1 + 1 x -00 x x x -+- 2 +1 0 0 + 11 x2 - x-1 1 ii. lim g(x) = lim x++ V x2 – x-1 X-1 x2 - x-1 X - 1 = lim x +oc x +0 - lim Vam M93001 (f) (2 pts) Write the equation(s) of all horizontal asymptotes of g. Write "none" if appropriate.

given the funcion F(x)=(x-1)^2/x^2+1

a) find the domain of the function in interval notation

b)Find the intercepts of the function. All work must be shown. Write your answer as ordered pair.

c) Find the equation of any asymptote.All work must be shown

d)Find the critical numbers.All work must be shown

e)Use the first derivative test to find the interval of increasing and decreasing. All work must be shown

f) Find the ordered pairs of the local maximum and minimum

g) Use the second derivative test to find the intervals of concavity and any inflection points. All work must be shown Including the number line with test numbers.

h) Graph the function on the grid provided. Label any intercepts, asymptotes,maxima,minima, and inflection points

MAT 1800 Midterm: MAT1800 Wayne State 1800 W18

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