Please help me with this. Please check if I've gotten the write answer for each questions. And if I have shown the correct steps. Just check part a) and b)Just write the answers that are correct (e.g. a) correct, b) incorrect )Image 1: The questionImage 2: My work SUNNATIVE JASKQUESTIONGrivon function: f(x) =2a) f(x)= x+15 10≤x < 42f(x+h) = (x+h) + 15f(x+h)-f(x)22= (x+h) +15 - X+152(x+15) - 2(x+h+ (5)(x+15) (x+h+15)! L' IN- 2x +36-2x-2h-30(x+15) (x+h+15)= -2h(x+15) (x+h+ (5)Nowlim f(xth)-f(x)h-70hturr-2hh-70 h(x+15) (x+h+15)= limh->0-2(x+15) (x+h+15)-2(x + 15) (x + 0 +15)2(x+15)²Therefore f'(x) =e1 x < 02X+15 10 ≤ x ≤ 4UXX ² + 3 X ²4xcosx2(X+15)22b) Now f'(x) = (x+15) ²-7 Differentiate with respect to 'x'(x+15) ² (0)-2x2(x+15)(x+15) 4-7f"(x) ==Therefore,4(x+15)³43f" (X) = (x +15) ³ / 0 ≤ x ≤ 44Thus f(3) =(3+15) ³= 4(18)31458 Consider the following piecewise function: f(x) =XCOLE x<00≤x≤4a. Use the first principles definition of a derivative to determine f'(x) when 0 < x < 4b. Determine f"(3)c. Determine the equation of the tangent to f(x) when x = - =d. Determine f'(x) when x > 4e. Is f(x) continuous when x = 4? Use the formal definition of continuity to argue your answer...

Answered: Image /qna-images/answer/02c13915-3fbe-4fc6-a09c-179bb011c448.jpg

Answered: Consider the following piecewise…

Consider the following piecewise function: f(x)= XCOSE xcoxx, x<0 0≤x<4 a. Use the first principles definition of a derivative to determine f'(x) when 0 < x <4 b. Determine (3)

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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Question

Please help me with this. Please check if I've gotten the write answer for each questions. And if I have shown the correct steps. Just check part a) and b)

Just write the answers that are correct (e.g. a) correct, b) incorrect )

Image 1: The question

Image 2: My work

SUNNATIVE JASK
QUESTION
Grivon function: f(x) =
2
a) f(x)= x+15 10≤x < 4
2
f(x+h) = (x+h) + 15
f(x+h)-f(x)
2
2
= (x+h) +15 - X+15
2(x+15) - 2(x+h+ (5)
(x+15) (x+h+15)
! L' IN
- 2x +36-2x-2h-30
(x+15) (x+h+15)
= -2h
(x+15) (x+h+ (5)
Now
lim f(xth)-f(x)
h-70
h
turr
-2h
h-70 h(x+15) (x+h+15)
= lim
h->0
-2
(x+15) (x+h+15)
-2
(x + 15) (x + 0 +15)
2
(x+15)²
Therefore f'(x) =
e
1 x < 0
2
X+15 10 ≤ x ≤ 4
UX
X ² + 3 X ²4
xcosx
2
(X+15)
2
2
b) Now f'(x) = (x+15) ²
-7 Differentiate with respect to 'x'
(x+15) ² (0)-2x2(x+15)
(x+15) 4
-7f"(x) =
=
Therefore,
4
(x+15)³
4
3
f" (X) = (x +15) ³ / 0 ≤ x ≤ 4
4
Thus f(3) =(3+15) ³
= 4
(18)3
1458

Consider the following piecewise function: f(x) =
XCOLE x<0
0≤x≤4
a. Use the first principles definition of a derivative to determine f'(x) when 0 < x < 4
b. Determine f"(3)
c. Determine the equation of the tangent to f(x) when x = - =
d. Determine f'(x) when x > 4
e. Is f(x) continuous when x = 4? Use the formal definition of continuity to argue your answer...

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