[question#1_partB] Evaluate the following limits. (Example solution is provided in the photo, kindly follow the format). USE OF L’HOPITAL’S RULE IS NOT ALLOWED. fa) - 2u sinh (x-1) ta - X=Note:DOM F(x) E IRf'(x) = (2xanh (x-1) +2²-x)f'(x) =d(2xsinh (x-1) + = (2x) - 2 / (x)dydxf'(x) = 2x coch (x-1) + 2² In (2) + 24h(x-1)- /('(x) is continuous on (0,1), therefore the function isdifferentiable on (0,1)f(0) = 2 (0) 6inh (0-1) +2°-0f(₁) = 2(1) sinh (1-1) +2'-1Fli) - 2 sinh lo) tflo) = 0+1 -0flo) = 1there is no x valueparallel tothe linea=0b=17where the tangent line at xisthat passes through the end pointslim x + -2²¯ f(x)= x³-4x²(x+2) ²(-2) ³ -4 (-2) ²(-2+2) ²8-4 (9)O= RHLsinceto reLALCLONT asyMPTOTES:lim x +∞x² +4x +4llencey = x- 8there forethere is a verticalJat x = -2(f(x)), lim x++oo (f(x)-ax)x³-4y² +xX³-√x²-x- 8x² -Uxlim x + 2+ f(x)= x³-Yv²(x+2)f(x) = (-2)² -4 (-2)²(-2+2)2O8y² +324 322 8x +32asymptote Evaluate the following limits. USE OF L'HOPITAL'S RULE IS NOT ALLOWED.log₁ (x+3)lim-11-cosh (cos¯`¹ x)x →1

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Answered: Evaluate the following limits. USE OF…

Math

Calculus

Evaluate the following limits. USE OF L'HOPITAL'S RULE IS NOT ALLOWED. log₁ (x+3) lim x →1 -1 1-cosh (cos ¹ x)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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[question#1_partB] Evaluate the following limits. (Example solution is provided in the photo, kindly follow the format). USE OF L’HOPITAL’S RULE IS NOT ALLOWED.

fa) - 2u sinh (x-1) ta - X
=
Note:
DOM F(x) E IR
f'(x) = (2xanh (x-1) +2²-x)
f'(x) =
d
(2xsinh (x-1) + = (2x) - 2 / (x)
dy
dx
f'(x) = 2x coch (x-1) + 2² In (2) + 24h(x-1)- /
('(x) is continuous on (0,1), therefore the function is
differentiable on (0,1)
f(0) = 2 (0) 6inh (0-1) +2°-0
f(₁) = 2(1) sinh (1-1) +2'-1
Fli) - 2 sinh lo) t
flo) = 0+1 -0
flo) = 1
there is no x value
parallel to
the line
a=0
b=1
7
where the tangent line at xis
that passes through the end points
lim x + -2²¯ f(x)= x³-4x²
(x+2) ²
(-2) ³ -4 (-2) ²
(-2+2) ²
8-4 (9)
O
= RHL
since
to re
LAL
CLONT asyMPTOTES:
lim x +∞
x² +4x +4
llence
y = x- 8
there fore
there is a vertical
J
at x = -2
(f(x)), lim x++oo (f(x)-ax)
x³-4y² +x
X³-√x²-x
- 8x² -Ux
lim x + 2+ f(x)= x³-Yv²
(x+2)
f(x) = (-2)² -4 (-2)²
(-2+2)2
O
8y² +324 32
2 8x +32
asymptote

Evaluate the following limits. USE OF L'HOPITAL'S RULE IS NOT ALLOWED.
log₁ (x+3)
lim
-1
1-cosh (cos¯`¹ x)
x →1

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