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
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2588b4fc-9812-409f-bd65-b8c86a5fc6bc%2Fec868f55-1824-4a23-a0d5-be6b50733320%2F1yoajw8_processed.png&w=3840&q=75)
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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