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Evaluate the following limits. 2x – (a) lim (2+ x) |3 – 6x| 1

Evaluate the following limits. 2x – (a) lim (2+ x) |3 – 6x| 1

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.6: Rational Functions
Problem 2E
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ll Fenercell ? 7:08 PM © 51% <Вack Homework for MATH131 МАTH131 Homework Fall 2020 1. Evaluate the following limits. 2x - 1 -2.r6 + 3x² + 2 3r4 – 2³ + 7 (a) lim (2+x) (f) lim I-2 (k) lim e-2/2 = 3 – 6z| I0+ sin z 1- cos r (1) lim e-3/1 - (b) lim I0 2x (g) lim I - 1 3x (m) lim In 2r = (c) lim I-2 (h) lim z+0 cos 5x tan 6x 4 - r (n) lim (In æ + e²) = - +2-3z r³ – 8 (d) lim 2 (i) lim z+2 x2 + r -6 (0) lim sin(e¬1/z²) = 2x (e) lim I0 3 VI +9 (j) lim (p) lim sin(tan-lx) = 2. Find the coordinates of the points on the curve y = x³ – x² – x +1 where the tangent line is horizontal. 3. Find dy/dr. () y = ** 1 3 (a) y = sin(tan x) (i) y = In V/x² +1 73 (b) x²y+y³ = 6 (f) y = e*in 2r (i) y = In(xe") (c) y = r² tan³1 (g) y = In(cos¬1 r) (k) y = x sin-1x+tan¬'(x²) 5 cos 2r (d) y = (h) y = (7x + 1)¬(2x – 7)* sec r +1 (1) y = xeVT=z² 4. Let if r <1 | x², if x > 1, f(1) = Use the definition of derivative to fin f'(1). If there is no derivative, explain why? 5. Discuss continuity and differentiability at r = -1 and r = 1. ise r <-1 Зr - 1, f(x) = { 22 + 5x, ise -1< r <1 ise r 2 1. 1 Özlem Orhan
Transcribed Image Text:ll Fenercell ? 7:08 PM © 51% <Вack Homework for MATH131 МАTH131 Homework Fall 2020 1. Evaluate the following limits. 2x - 1 -2.r6 + 3x² + 2 3r4 – 2³ + 7 (a) lim (2+x) (f) lim I-2 (k) lim e-2/2 = 3 – 6z| I0+ sin z 1- cos r (1) lim e-3/1 - (b) lim I0 2x (g) lim I - 1 3x (m) lim In 2r = (c) lim I-2 (h) lim z+0 cos 5x tan 6x 4 - r (n) lim (In æ + e²) = - +2-3z r³ – 8 (d) lim 2 (i) lim z+2 x2 + r -6 (0) lim sin(e¬1/z²) = 2x (e) lim I0 3 VI +9 (j) lim (p) lim sin(tan-lx) = 2. Find the coordinates of the points on the curve y = x³ – x² – x +1 where the tangent line is horizontal. 3. Find dy/dr. () y = ** 1 3 (a) y = sin(tan x) (i) y = In V/x² +1 73 (b) x²y+y³ = 6 (f) y = e*in 2r (i) y = In(xe") (c) y = r² tan³1 (g) y = In(cos¬1 r) (k) y = x sin-1x+tan¬'(x²) 5 cos 2r (d) y = (h) y = (7x + 1)¬(2x – 7)* sec r +1 (1) y = xeVT=z² 4. Let if r <1 | x², if x > 1, f(1) = Use the definition of derivative to fin f'(1). If there is no derivative, explain why? 5. Discuss continuity and differentiability at r = -1 and r = 1. ise r <-1 Зr - 1, f(x) = { 22 + 5x, ise -1< r <1 ise r 2 1. 1 Özlem Orhan
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