Q1/ Answer the following: (a) Show that sin-x + cos-1x = " 2 x(x-y) (b) Find the value of tan-1 tan-1 2, where >-1 y(x+y)
Q1/ Answer the following: (a) Show that sin-x + cos-1x = " 2 x(x-y) (b) Find the value of tan-1 tan-1 2, where >-1 y(x+y)
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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![Q1/ Answer the following:
(a) Show that sin-1x+ cos-1x =
x(x-y)
(b) Find the value of tan-1
tan-
where
> -1
y(x+y)
Q2/ Answer the following:
(a) Is Rolle's Theorem applies for the function f (x) = cos(sinx) on the closed
interval [-1,1]? If it can be applied, then find the value(s) of the constant(s) c.
(b) Let f(x) =
sin (cos-1 (sin(cos-1Vx ))). By using chain rule, show that
f'(1) =
Q3/ Answer the following:
(a) Express sin(2 cosx) in an algebraic form. Furthermore, sketch this
function and find its domain and range.
csc2 (2cot-1Vx)
(b) Show that J
x-1
dx =
2 Vx
+ c.
Vx+x Vx
Q4/ Answer the following:
(a) Simplify the function y = |x – 1| + |x + 1|. Moreover, compute the definite integral
L(1x - 1| + |x + 1|) dx. Is this function differentiable at x = -1? Explain that.
(*) (i) Find
3x2+x+1
sin-)+sec-1(x)
d
(b) (i) Compute lim cot-1
3x2-7
dx
tan-1x+tan-1
x+00
Q5/ Answer the following:
(a) Compute the following limits:
x3+x2 +x+1
sec-1(V2+h)-sec-1/2
(i) lim
x-1
(ii) lim
h-0
x2-1
h
cos
x + 2
(b) Test the continuity of the function f (x) =
x-2
at the point x = 2.
x = 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3cf1c3b3-a09c-4011-b05e-9e1514d186e9%2F92b9155f-bbb7-4502-ba47-df35be077caa%2Fo7ujqh2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1/ Answer the following:
(a) Show that sin-1x+ cos-1x =
x(x-y)
(b) Find the value of tan-1
tan-
where
> -1
y(x+y)
Q2/ Answer the following:
(a) Is Rolle's Theorem applies for the function f (x) = cos(sinx) on the closed
interval [-1,1]? If it can be applied, then find the value(s) of the constant(s) c.
(b) Let f(x) =
sin (cos-1 (sin(cos-1Vx ))). By using chain rule, show that
f'(1) =
Q3/ Answer the following:
(a) Express sin(2 cosx) in an algebraic form. Furthermore, sketch this
function and find its domain and range.
csc2 (2cot-1Vx)
(b) Show that J
x-1
dx =
2 Vx
+ c.
Vx+x Vx
Q4/ Answer the following:
(a) Simplify the function y = |x – 1| + |x + 1|. Moreover, compute the definite integral
L(1x - 1| + |x + 1|) dx. Is this function differentiable at x = -1? Explain that.
(*) (i) Find
3x2+x+1
sin-)+sec-1(x)
d
(b) (i) Compute lim cot-1
3x2-7
dx
tan-1x+tan-1
x+00
Q5/ Answer the following:
(a) Compute the following limits:
x3+x2 +x+1
sec-1(V2+h)-sec-1/2
(i) lim
x-1
(ii) lim
h-0
x2-1
h
cos
x + 2
(b) Test the continuity of the function f (x) =
x-2
at the point x = 2.
x = 2
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