(1) Find the local linear approximation of f(x) = ln (5-4x) at xo = 1 and use it to estimate the value of In (0.98). (A) f(x) ~ L(x) = x - 1 and ln (0.98) = -0.020 (B) f(x) ~ L(x) = 4x - 4 and In (0.98)= -0.020 (C) f(x) L(x) = -4x - 4 and In (0.98) = -0.020 = -0.020 (D) f(x) ~ L(x) - 4x + 4 and ln (0.98) = =
(1) Find the local linear approximation of f(x) = ln (5-4x) at xo = 1 and use it to estimate the value of In (0.98). (A) f(x) ~ L(x) = x - 1 and ln (0.98) = -0.020 (B) f(x) ~ L(x) = 4x - 4 and In (0.98)= -0.020 (C) f(x) L(x) = -4x - 4 and In (0.98) = -0.020 = -0.020 (D) f(x) ~ L(x) - 4x + 4 and ln (0.98) = =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(1) Find the local linear approximation of f(x) = ln (5-4x) at xo = 1 and use it to estimate the
value of ln (0.98).
(A) f(x) ~ L(x) = x - 1 and In (0.98)= -0.020
(B) f(x) ~ L(x) = 4x - 4 and In (0.98)= -0.020
(C) f(x) ~ L(x) = -4x - 4 and In (0.98)= -0.020
(D) f(x) ~ L(x) = -4x + 4 and In (0.98)= -0.020
(2) Let f(x) = x³ - 2x, find Ay and dy for x = 1 and Ax = dx
dx = 0.1.
(A) Ay = f(1.1) - f(1) = -0.869 - 1 = -1.869; dy = f'(x)(dx) = (3(1)² - 2) (0.1) = 0.1
(B) Ay = f(1.1) - f(1) = -0.869 - (-1) = 0.131; dy = f'(1)(0.1) = 0.1
-
(C) dy = f(1.1) − f(1) = -0.869 - (-1) = 0.131; Ay = f'(1)(0.1) = 0.1
(D) Ay ~ dy = f'(1)(0.1) = 0.1
Questions No.3 and No.4 refer to the following: Let f(x) = 5-2x. If g(x) is a fun
with derivative given by g'(x) = f'(x) f(x) (x+3).
(3) On what interval(s) is g(x) increasing?
-3]U[/2/2, ∞0)
(B) [-3, 9]
(^)(
(C) [, ∞)
(D) cannot be determined](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba01848d-09ed-47b0-8866-1aec132e3933%2F1f230cbf-37c3-4367-898c-83e1cf6b9414%2Fy0n3es7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(1) Find the local linear approximation of f(x) = ln (5-4x) at xo = 1 and use it to estimate the
value of ln (0.98).
(A) f(x) ~ L(x) = x - 1 and In (0.98)= -0.020
(B) f(x) ~ L(x) = 4x - 4 and In (0.98)= -0.020
(C) f(x) ~ L(x) = -4x - 4 and In (0.98)= -0.020
(D) f(x) ~ L(x) = -4x + 4 and In (0.98)= -0.020
(2) Let f(x) = x³ - 2x, find Ay and dy for x = 1 and Ax = dx
dx = 0.1.
(A) Ay = f(1.1) - f(1) = -0.869 - 1 = -1.869; dy = f'(x)(dx) = (3(1)² - 2) (0.1) = 0.1
(B) Ay = f(1.1) - f(1) = -0.869 - (-1) = 0.131; dy = f'(1)(0.1) = 0.1
-
(C) dy = f(1.1) − f(1) = -0.869 - (-1) = 0.131; Ay = f'(1)(0.1) = 0.1
(D) Ay ~ dy = f'(1)(0.1) = 0.1
Questions No.3 and No.4 refer to the following: Let f(x) = 5-2x. If g(x) is a fun
with derivative given by g'(x) = f'(x) f(x) (x+3).
(3) On what interval(s) is g(x) increasing?
-3]U[/2/2, ∞0)
(B) [-3, 9]
(^)(
(C) [, ∞)
(D) cannot be determined
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