Find the indicated difference quotient and simplify your answer. f (x) = x 3 +3x, f (x +h)− f (x) /h , h does not equal 0  f (x) = 1 /x2 , g (x)− g (3) /x −3 , x does not equal 3. f (t) = 1 / t −2 , f (t)− f (1)/ t −1 , t does not equal 1.

Q: 2. . If f(x) dx = 4 and 3g(x) dx = -9, evaluate [² [3f(x) + g(x)] dx

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Q: 3) Let f(x) represent the path of a particle. x* 1 f(x) =+ x 2 1 16 2x2 Suppose the particle starts…

A: The arc length = the distance covered along the curved path f(x).  A = the arc length  A =…

Q: 3 – x2, 0<x < 1 | f(2) dr, where f(x) = 1<r< 2.

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Q: Q2) Find the values of constants (a)&(b) that makes the f(x)= ax + b 3 (-3 x≤-2 -2<x<4 x24 Con

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Q: 클 ~D f(x) = x² e² е (12) Find f '(x). f'(x) = x²²²e² + e² 2x² f" (x) = X

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Q: Find the particular solution determined by the given condition 314 f'(x) = 3x -6x; f(1) = -6 II

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Q: Find f(x) by solving the initial value problem s'(x) = 4x2-5, f(0) = -3 %3D

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Q: The antiderivative of the function f(#) + 8* is -8 + 2.0a2 +e 4 +4.0a2 +c -4 + 16.0a? + c -4 4.0a2 +…

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Q: 13 Given that f(x)= 2x+1 and h(x)=x, find (h o f)(3).

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Q: Solve f(x) is greater than or equal ro 0 f(x) = x2 + 6x - 7 over x2 -10x + 25

A: We have to solve for the function f(x) when f(x)≥0. Given function -  f(x)= x2 + 6x - 7x2 -10x + 25

Q: 4. Given the functions h(x) = 3x - 4 find h(x) 5x + 2

A: Here we have to find inverse of function h(x).

Q: Find the value of C such that the fnction Continubus on (-00,00) Cx +1 for XS 2 f(x)= r4x+I-3 for…

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Q: For which values of c does f (x) = x2 + cx + 1 have a double root? No real roots?

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Q: Given f()= 2x + 1 and ()= r*+ 2x-1, fnd (f- (1).Then valute the difence when x=2.

A: Sum and difference of the two functions

Q: (b) Given f(x)=9x – 6x² + x. Find F(x) dx in the form a In|g(x) + h(x)], where a is a constant

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Q: The function f(x) =x³ – 3x2 + 3x -1, x e R has a point of inflection | at A) x = 1 B) x =-1 C) x = 3…

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Q: 1. Solve for the values of x in the function below. f(x)=x3-4x-0.5x2+2

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Q: 8. For f(x) = -4x + 5, find the solution to f(x) = 41.

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Q: 10.Given f(x)=2x-3 and g(x)= x² + 1, solve f[g(x)]

A: We have to find fgx where functions are given as: fx=2x-3 and gx=x2+1. Here we have to find…

Q: Use the linear approximation (1 + x)k = 1 + kx to find anapproximation for the function ƒ(x) for…

A: Given: ƒ(x) = (4 + 3x)1/3

Q: 6. 9. 6, If f(x) dx = 31 and g(x) dx = 18, find [4f(x) + 5g(x)] dx.

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Q: 6. Given f (x) = 6x – 4, solve for x for which f (x) = 7 -

A: For the given f(x), equate f(x)=7.

Q: (2) GIVEN: f.R- R, Sx) = x²(3x– 1). Find f'(x) in factored form.

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Q: 1. Find f'(x) when f (x) = ln(1 – x²) + 3sin-1x + V1 – x² + 7. | Write your answer as a single…

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Q: From Variation of parameters for the 2 -1 X' X + e 3 -2

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Q: 2. Given f(x) = –vx + 2 and g(x) = x² – 2x + 7. What is the domain of q (x) = f(x) – g(x)? a. Can't…

A: Topic- function domain

Q: For /- (x+x³) (x Tan-lx+1) dx = In[F(x)]+C• What is f(/3) if C = 0? -1 3 -1 + + + -15-15-15

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Q: 2 Given that f(x) = 4x – 7 and g(x) = 4 – a?, calculate (a) f(g(0))=| (b) g(f(0))=|

A: Answer(a): The given functions are: fx=4x-7 and gx=4-x2. Then, the composition function is given as:…

Q: Find the most general antiderivative of f(æ) = -5x + (1 – a²)-1/2, where -1 < x < 1. F(x) =

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Q: 8. Find (f+g)(x). f(x) = 5x² – 9x + 8 g(x) = &r2-7x + 2 A) (f+g)(x)= 13x - 16x + 10 B) (f+g)(x)=-3x…

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Q: f(x)=9x^3+8x^2+7x+3 F has a candidate to a point of inflection in x equals_____

A: Given function f(x) = 9x^3+8x^2+7x+3 Differentiating on both sides with respect to x f'(x) =…

Q: 10. For f(x) = 2x3 + 7x + 4, g(x) = 4x? + 4x + 6, and h(x) = 6x² + 3 in Zg find f(x) + g(x)h(x) with…

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Q: Find the solution using homogenous function substitution of the following DE Show that 2xyy' == x² +…

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Q: How do I find the possible inflection points of f(x)=a/((x^2)+(b^2))? It also states a and b are…

A: To find point of inflection we need to find x from f"(x)=0

Q: 1. Solve for the variable x. F = kx – kxo A. x=F-kxg А. х- O B. x=F-kx, k F- Kxo О с.х3 C. x= D.…

A: The given equation is F=kx-kx0

Q: 3. If f'(x)= 3x² 2 and f(1) = 4, find f(e).

A: To find f(x) from f'(x) we integrate it C=integrating constant

Q: Find the derivative and simplify. -x² + 7x + 1 d. 2x° -x +7x+12 Choose the correct answer below What…

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Q: The function f(x) 223 42x? + 240x – 11 has two critical numbers. The smaller one is x = and the…

A: Let's find.

Q: 5. Find the antiderivative of the function and check your answer by differentiating. f(x) = 9x +…

A: 5. We need to evaluate the antiderivative of the following function fx = 9x+15x-2

Q: Find the general antiderivative of f(x) = 4e* - 3x-2 and check the answer by differentiating. (Use…

A: Given, f(x) = 4ex -3x-2 We have to find  ∫f(x)dx

Q: 02. Find the end behavior for y = x–9x+20. A. x + +0, f(x) → +∞ ; x → -o, f(x) → +∞ B. x → +0,…

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Q: f(x) : == - x2, with domain [2, +o) %3D

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Q: Which is equal to (2) (x) given that g(x) = 1 – 3x and h(x) = Vx? Vx – 3xVx 3x/x - Option 1 Option 2…

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Q: Find the absolute extrema of fGx\=x. %½x°- 2 x+1 on the interval E1,2I.

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Q: Determine the value of ∫k4 f(x) dx given that ∫49 f(x) dx=−9 and ∫9k f(x) dx=−3.

A: We have to find following definte integral .Information is given below:

Q: (-4x-12) dx (x+10) (x-4)- For F()- 1. What is F(3)? %3D

A: Option A

Q: If f(x) = 4 – x² & g(x) = vx then find (fog)(x) » (gof)( x + 8 If f(x) = 3x – 8 & g(x) = then find…

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Q: What is the value of f(1) - 168 in x3 Inx dx = f(x) ((1/4) Inx - B) + C? 02 8 8 0 3 1

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.