Show that the function F(x) = (x - a)2. (x - b)2 + x takes on the value (a + b)/2 for some value of x.

Q: Let f(x)= (x^3+3x+2)^2 f'(5)= ?

A:

Q: What is the domain of the function f(x)=x/x²-1?

A:

Q: Find the domain of f

A: Given: fx=9-x2

Q: Is f(x)=x^2-2x even or odd ?

A:

Q: Find the point at which the line f(x) = 3x – 9 intersects the line g(x) 3x + 9 -

A: The function f(x)=3x-9 and g(x)=-3x+9 intersects when f(x)=g(x).

Q: 1. How to define the function, f(x, y) = 15x+4x*y+15y 3x+3y to make it a continues function?

A: We have to find the given function is continuous.

Q: What is derivation of f(x) = (2x² – x + 1)³ at %3D Xo = 1 ?

A:

Q: 2. Determine f'(1) for the function f(x) = (8x – 6Vx5 + 3) (x² – 9x² +) -

A: A detailed solution is given below

Q: Зах + 3 for x -2

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Q: what is (f +g)(x) given that f(x) = 3x+4 and g(x) = 2x-5?

A:

Q: Can you calculate f(0) for the function f(x) = 2π2?

A: Answer is  f(0)=2π^2. Explanation is given below

Q: How are the zeros of g(x) related to the standard form of the function?

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Q: Find a, b to Continue The function at x=35 * >3 3 X = 3 ax+b flx) = 2a-b+1 bx-a+3 X3

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Q: Let f(x)=3x^2+7x-4 and g(x)=9x^2-5x+1. Which equation shows h(x), where h (x)= f(x)-g(x)?

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Q: Find the function f(x) such that f'(x)=3e-2x-6x2+1 and f(0)=2

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Q: Find the points of inflection of the function f(x)=x2 / 1+x2.

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Q: Find the function f(x) that satisfies the conditions f1) - | and f'x)= 2x+1

A: Given that: f(x) satisfies f(1)=1and f'(x)=2x+1(x2+x+1)3 We have to find the function f(x)

Q: snip

A: Given: f(x)=x3-3x2

Q: Can you calculate f(−2), f(x + 5), f(α), and f(α + Δ) for the function f(x) = 2π2?

A: The given function is: f(x) = 2π2. Yes we can calculate  f(-2) and other values f(x+5), f(α) and…

Q: snip

A: Concept - If there is function f(x), then for f(x) to be defined the numerator should never be…

Q: What happens to the function f (x) = (x – 1)² + 1 when it becomes f'(x) = (÷r – 1)² + + 1?

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Q: What is f(x^2)? *

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Q: Consider the function: f (x) = 3 |x|+x2 – 1 Find f(-2) exactly

A: Given:- f(x) = 3|x|+x2-1 To find:- f(-2)

Q: Find f(0), f(-3), f(2x+3) for the function f(x)= -2x^2+x-1.

A:

Q: Explain why the function has at least one zero in the given interval.

A: The given function is f(x)=x3+5x-3 ,  0,1

Q: Find the domain of the function.

A: Domain is set of all the input values which can take value in function such that it gives some…

Q: what is the value of f’(0) if f’(x)=(x^2-2x-1)^2/3?

A: We have to find value of f'(0).

Q: The linear approximation of the function f (x) =90– 55x at x=2 is: 90-55x -20+55x 110+55x 110-55x

A:

Q: Linearize the function f(x) = x3 + 2x + 4 at a = 3.

A: To linearize a function  at certain point x=a , first we need to evaluate the function value at a (…

Q: Consider the function F(x)= (x+2)^2 for the domain [-2, ∞)

A: Given           Function is :                            F(x)=(x+2)2 for the domain [-2, ∞)   To…

Q: 8. For the function: f(x) = x² - 7x - 4 find f( - 5)

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Q: Find a,b to continue the function at x=3 if: x > 3) x = 3 x < f(x) = ax + b 2ab + 1 bx - a +3 3)

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Q: Given the funci f(x + 1) = f(x) + f( – 3) = %3D - ||

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Q: What value of b completes the function f(x) = −x2 + bx + 1?

A: We have to find the value of b that completes the function f(x)=-x2+bx+1.

Q: Explain why f(x) satisfies the Intermediate Value Theorem. f(x)=ex - x3 - 8

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Q: Find the domain of the function in interval notation: f(x) = Vx + 8

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Q: differentiate find f'(t) for f(x)=(2x-2)(3x^3-x^2+1)

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Q: Find the domain of the function in interval notation: f(x) = Vx + 22

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Q: Express the function in the form  f ° g    F(x) = (2x + x2) 4

A: Given, F(x) = (2x + x2)

Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.

A: Topic = Functions

Q: Consider the function y = 3x2+2x-4. What is the exact value of C in the interval [-2, 4] such that…

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Q: Show that the function f (x) = x* + 3x + 1 has exactly one solution in the interval [-2, -1].

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Q: Determine where f(x) = x² – 2 is increasing and where it is decreasing.

A: Given: fx=x2-2 The graph of the given equation is,

Q: Differentiate the function with respect to the independent variable. f(x) = - 3x° + 4x$ – 7

A:

Q: Find the absolute maximum and minimum values ​​of the function f(x)=x2−3x2+1 in the interval [-1/2,…

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Q: What is the linear function of f(x)= -1/2x

A: Linear function

Q: Let f(x)=(5)x+1. Which is equal to f(−3)?

A:

Q: f(x) = x²+6x+5 2-1

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

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.