13. f(x) = √x₂ -π≤ x < 0, 10, 0

Q: 3x-4 -,x < 1 x+2 4. Given the function f (x) = . Calculate f'(1-) and f'(1+). In?x x+1

A:

Q: Show that if f (2) = −2 and f'(x) ≥ 5 forx &gt; 2, then f (4) ≥ 8.

A: Given that f (2) = −2 and f'(x) ≥ 5. And also, f(4) ≥ 8.

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: Find all functions y satisfying y" + y" = y' + y. You may use the factor- ization x + x² – x - 1 =…

A:

Q: 3x10 + 3a5 + 5æ² + 7. What particular solution that satisfies Suppose f'(x) 455 -? 66 f(1)

A:

Q: Let f(x)=√1+4x f'(3)

A: We know that the derivative of x^n=nx^(n-1)

Q: 3.) flx) x+2

A:

Q: Find f'(x) for f(x) = ex²+3x+¹¸

A: Given that f(x)=ex2+3x+1

Q: Suppose, f'(x)=2cosx+ sec x, -7<x<7½, and it is known that f(T) =D4. Find the function f(x). IT

A: Integrating on both sides, we get

Q: 9. Use the Intermediate value theorem to show that f(x) = 2x( – 3 has a zero in the interval [1,2].

A:

Q: f (æ, t) = e-t function fea - fu = 0 provides equality. True False

A: Given the function fx, t=ex-t We need to check the validity of fxx-ftt=0 to get the correct option.

Q: Show that f(x) = x³ − x² − 3x + 1 has a zero over the interval [0, 1].

A: given function We need to sow that function has a zero on given interval.

Q: Utt u(x, 0) ut (x, 0) = = = 4uxx x² + 3x

A: USIND D'ALEMBERT'S SOLUTION FOR ONE DIMENSIONAL HOMOGENOUS WAVE EQUATION ,WE HAVE

Q: 25. f(x)=2x, 0<x<2

A: 25 Given function is fx=2−x, 0&lt;x&lt;2. We have to find the even and odd extensions of the given…

Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

A:

Q: 1. (Bx2 |x- 61-8 for x> 2 (a) For what value of Bis the function f(x) = }", for x 2 continuous atx=…

A:

Q: ind the interval of increase and decrease of the following functions: ii. f(r) = r°(5 – r)? vi. f(x)…

A: As per guidelines we can solve only three subpart. For any other questions repost them.

Q: Let f(x) = x³ + √√. Then f'(1) = 02 O 1.5 O 3.5 04

A:

Q: 3- Find the root of function F(x) = x² – 10 Using XL=3 , X,-4 , ɛ = 0.1

A: given function Fx=x2-10 with condition XL=3, Xu=4, εS=0.1 claim- find the roots of the function

Q: If f (x) = sin 2x , find all of the stationary points of f (x) on 0<x<2n

A:

Q: a) Let f(x) = √5 + 132³. Find f'(x). f'(2) - O b) Let f(z) J'(x) = 0 evS+13³ Find f'(z). -e'

A:

Q: 3. Let f(x) = { ,x<2 ax + b, x22 Find a and b so that f (2) exists.

A: To find the value of a and b

Q: 3. Find algebraically the zeros for f (x) = x - 4x 9x + 36x %3D

A: Given function

Q: 3. Over which interval is the function f (x) = 1 + 2ex -3x increasing?

A:

Q: 03: Let S(x)=12-x-1|-1. -1. Find f"(0) and Find f'(4)

A:

Q: 8. Simplify f(x + h) - f(x), where: a) f(x) = 2x + 3 b) f(x) = 1 c) f(x) = x² %3D 1 2.

A: a) f(x)=2x+3b) f(x)=x2c) f(x)=11

Q: Given f (x) = x³ - 3x – 1,x 2 2, find (f~')'(-1)

A:

Q: Express the function in the form fog. (i) F(x) = (2r + r*)ª. (ii) F(r) = %3D 1+ VE

A: Answer

Q: Find the approximate integral of the following function using Simpson's 3/8 rule and determine the…

A: The function given to us is as follows: fx=x+1x2+1 at  x=0, 3 We are asked to find the integral of…