Evaluate the following: -1 x-1(x+1) xả-5x-20 x-5 x²-4x-5' x-5 lim x-5x²-10x+25² i. lim ii. lim iii.
Evaluate the following: -1 x-1(x+1) xả-5x-20 x-5 x²-4x-5' x-5 lim x-5x²-10x+25² i. lim ii. lim iii.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![2.
a) Evaluate the following:
-1
x-1(x+1)'
xả-5x-20
x-5 x²-4x-5'
x-5
i. lim
ii. lim
iii. lim-
x-5x²-10x+25
√x²+4-2
x²
5h+4-2
iv. lim
x-0
V. lim-
h→0 h
b) Find the derivative of the following functions:
i. f(x) = -secx +
1
- secx
ii. f(x) = x-5 tan 4x +
sin 4x
x
iii. f(x) = ln(x-¹) [sinx + √x² + 1].
iv. f(t) = 3t² cost - t³ sin √t,
e2x In(x²-3x+8)
v. f(x) =
(x+1)²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c1037fb-de73-4414-8ea5-0ceb87e3d27b%2F2a793bab-d9af-4c55-b632-307abfbcd07e%2Fid3a3x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.
a) Evaluate the following:
-1
x-1(x+1)'
xả-5x-20
x-5 x²-4x-5'
x-5
i. lim
ii. lim
iii. lim-
x-5x²-10x+25
√x²+4-2
x²
5h+4-2
iv. lim
x-0
V. lim-
h→0 h
b) Find the derivative of the following functions:
i. f(x) = -secx +
1
- secx
ii. f(x) = x-5 tan 4x +
sin 4x
x
iii. f(x) = ln(x-¹) [sinx + √x² + 1].
iv. f(t) = 3t² cost - t³ sin √t,
e2x In(x²-3x+8)
v. f(x) =
(x+1)²
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