10 If f is a continuous function and F(x)=f(x) for all x€R, then | f(Gx)dx=?

Q: Suppose f is continuous everywhere, and | f(x) dx = -1 and 3 Find f(2)dz. f(x) dx 2. Find dx. Cannot…

A: As per our guidelines we are supposed to solve only one question i.e. the first question. For the…

Q: x+2 x<2 1) Let f(x)={ ax² – bx+3, ; 2sx<3 x 23 2x-a+b Find the values of the constants a and b given…

A: Here I am attaching image so that you understand each and every step.

Q: (2x+1 x² +2 x> h) Xsh Q3) If the function f(x) %3D having limit at x h. Find the value of h.

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Q: + [ƒ(2)₁ Suppose that fand gare continuous functions such that 1 [ g(x)dz -3, find f(x)dx= 2 and +…

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Q: 1) Find the value of C that make the function continuous at x-1? x 1 -

A: We have given piecewise function  Function is continuous at x=1 if  f1+=f1=f1- f(x) = C-x        if…

Q: ,15 15 ** Let f be a continuous function. If f(x)dx = 15 and f(x)dx = -8, then f(x)dx equals -5 В C…

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Q: 6. If f is continuous and f(x)dx=4 , '3 | xf(x?)dx=

A: Explained below

Q: 25 If f is continuous and f(x) dx = 8, find xf(x²) dx.

A: given ∫025f(x)dx=8∫05xf(x2)dx=?

Q: The derivative of the function f(x) =x ln x is: a. f'(x) = In x +1 b. f'(x) = ln x +. c. f"(x)= In x…

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Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: 11. Suppose a function is defined so that it has derivatives f'(x)=x²(1–x) and S"(x)=x(2-3x). Over…

A: Given that, the derivatives of a function f is defined asf'x=x21-xf''x=x2-3x We need to find the…

Q: 10 If f is continuous and f(x) dx = -15, evaluate f(5x) dx. %3D

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Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x2 + 5x…

A: This is a limit and continuity problem

Q: 81 xf(x²) dx. 6. If f is continuous and f(x) dx = 4, find

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Q: 3. The graph of the continuous function g, the derivative of the function f, is shown above. The…

A: Given problem is :

Q: 4 Suppose that f(1) = 9, f(4) = -7, f'(1) = 6, f'(4) = -1, and f" is continuous. Find the value of…

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Q: x? Find the critical points of the function: f(x)= x- 2

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Q: (3) If the functions f(x) and g(x) are continuous 0sxS1, then f(x)/ g(x) is continuous on the…

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Q: 36 6. If f is continuous and f(x) dx = 2, find xf(x²) dx. %3D

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Q: Find the critical points of the following function.   f(x) = 1/x - ln(x)

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Q: Зx2 — 1 if x 1 Determine c and d so that f is continuous everywhere

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Q: -2 x< -1 Q1)a) For what values of a and b is g(x) = ах — b -1<x<1, x21 Continuous at x= -1

A: The suitable formula for continious       LEFT HAND LIMIT = RIGHT HAND LIMIT

Q: (x²-x for x +0 If f(x) : and if fis continuous at x = 0, then k= 2x f(0) = k -1/2 O 1/2 O 1

A: f(x) = (x2 - x)/2x limx→0 x2-x2xlimx→0 x(x-1)2xlimx→0 x-12= -12

Q: 1) Find the value of Z that make the function continuous at x=4? V-2 x + 4 X-4 f(x) = {z3 x = 4

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Q: 25 If f is continuous and f(x) dx = 12, find xf(x?) dx.

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Q: V4+x-2 If f(x) = ,x*0 be continuous at x = 0, then f(0) = 1/2 1/4 3/2

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Q: If F(x) is a differentiable function with derivative F'(x)= Enx"-1 and F(0)=0, then F n=2 x2-x O 1-x…

A: Introduction: For a differentiable function fx, if f'x is given, then integrating both sides, fx can…

Q: '12 9. If f is continuous and f(x) dx = 20, find f(2x) dx.

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Q: 4ex +x-k if x 0 be continuous everywhere?

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Q: Find numbers a and b, and c, so that f is continuous and differentiable at every point. 4) x- + C,,…

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Q: A function y = f(x) is continuous and differentiable on the interval (0, 7). If f(x) dx = 13, f(1) =…

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Q: A continuous function y = ƒ(x) is known to be negative at x = 0 and positive at x = 1. Why does the…

A: Given that f(0)&lt;0 and f(1)&gt;0  f(x) is a continuous function.

Q: 10 If f is a continuous function and F(x)=f(x) for all x € R, then x)dx=? A © FS) - F)] B ©2[F(5) –…

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Q: 18 9. If f is continuous and f(x) dx = 14, find f(2x) dx. !!

A: Solution is in step 2

Q: If f(x) is a twice differentiable function with •1 f(0) = 5, f(1) = 4, f'(1) = 2, Then So 2x f"…

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Q: 1(a): Find the value of k that makes function continuous at x = 4 4x +8 > 4 4x – k a <4 f(x) =

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Q: 10 If f is a continuous function and F'(x)=f(x) for all x € R, then dx=? @2[F(5) – F(1)] ®2[F(10) –…

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Q: If the derivative function of f(x) is continuous on [1,2], and f(1)=1, f(2)=4. Find * O 2 O 24 O 4 O…

A: We will use substitution to solve this

Q: 12. Suppose we know that f (x) is continuous and differentiable on the interval [1,9], that f (9) =…

A: To find: The largest possible value of f1. Given: The fx is continuous and differentiable on the…

Q: S x2 – 3 |kV5+x _if x > –1 if x < -1 - 2. Determine the constant k such that the function f(x) : is…

A: As per our guidelines, I can answer one question and maximum three subparts of a question. Since you…

Q: 9 3 Iff is continuous and f(x) dx 8, find f(x2)dx

A: Given as

Q: 10 If f is a continuous function and F'(x)= f(x) for all x ER, then x)dx=? (в F6) - F)] B O2[F(5) –…

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Q: 3. Find constants A and B such that the function x2 f(x) = if x 2 is differentiable at x = 2.

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Q: The function if x 1 has critical points at... (Choose all that apply.) x = 0 x = -1 x = 3

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Q: x-1 for x 1 x -1 show that flx) is continuous at x = 1 !3! for x 1,

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Q: 8. If the derivative function of f(x) is continuous on [1,2], and f(1)=1, f(2)=4. Find* O 15 02 24

A: The given integral is: I=2∫12f(x)f'(x)dxLet, f(x)=t⇒f'(x)dx=dtWhen, x=1⇒t=f(1)=1When,x=2⇒t=f(2)=4

Q: 19 If f(x) be continuous function for all real values of x and satisfies; x2 + {f(x) – 2 }x + 2/3 –…

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Q: 1. If y = f(x) is a continuous function for all 0 <x< 6, and f(0) = 1 and f(6) = 7, then which of…

A: We use the given graph of the function y=f(x), to answer the given question.