Using divided difference formula, we calculated a, to be 1. If x; - x;-1 = 1, and f (x,) = f (x2), then f(x,)- f(x1)=4 Select one: True False

Q: Let f(x) = x³ + x + 4 and g(x) = 2x +3 in Zs[x]. Then, upon dividing f(x) by g(x), we get The…

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Q: If f(1) =1 and f (x) 2 3 for 1 <x < 3, how small can (3) possibly be?

A: We will find the smallest possible value of f(3) as following.

Q: If f(z) = 7(x – 1) + 8 , what is the value of f(1) ? %3D

A: Given : f(x) = 7(x-1) + 8 To find : f(1) = ?

Q: Given the function: f(x)= (x^2-2 where, x/=4). Calculate: f(4)

A: This question is based on functions define in an interval.

Q: f(x)=(x2+3x+7)4, then f'(x) =    f'(1) =

A: We have to find derivative

Q: given f(x)=x4-8x2+2, find all x-values such that f(x) has horizontal tangent lines

A: Compute the derivative of the given function.

Q: 10. If f (x) = 2x(1+In(2x)), and f'(c) = 6, find c.

A: Given function is fx=2x1+ln2x. Product rule of differentiation states that: ddxuv=vddxu+uddxv…

Q: If f(x) = 4x2 + 1 satisfies Rolle's Theorem on [a, 2], then a = 2 -1 -2 none

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Q: Given f' (x) = e* · (x² + 5x +6), and f" (x) = e* · (x² +7x + 11), Find f (x) given that f (0) =1

A: First integration and then satisfied condition

Q: Given g(x) = In(7x5 + æ), the derivative g'(x) is 5x4 35x4 +1 7x5 + I O 7z5 +x 7x +I 35x4 +1 O 35x*…

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Q: If f(x, y) = In (2x-3y), then find of ||

A: We can solve this problem using partial derivatives.

Q: Generate the approximation formula 1 f'(x) × - [4f(x+ h) – 3f(x) – f(x+2h)] 2h with the error term.

A: The objective is to generate the approximation formula,

Q: Find f(x) if f′′′(x)=3x such that f(3)=12, f(5)=25 and that at x=4, the point of inflection will be…

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Q: Given that f(x)=x^2+8x+15f(x)=x2+8x+15 and g(x)=x+5g(x)=x+5, find f(x)\div g(x)f(x)÷g(x) and express…

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Q: and f(a) f(x) = 4x² + 5x² + 6x-7 3 7 2. Find f(x), f"(0), given

A: Given a function f(x)=4x3+5x2+6x-7 We have to the following of the given function, f''(x) f''(0)…

Q: Given f(x) = By using long division or otherwise, show that f(x) 2x - 3 r(x - 1)(2x + 3) x(x - 1)(2x…

A: What is Partial Fraction: Partial fraction is the tool to write a rational function into a sum of…

Q: If f(x)=ln(6x3+3x2+3x+3), find f′(x).

A: given function :

Q: Given that f(x) = 4x+1 and h(x) = x°, find (h o f)(2).

A:

Q: For what values of x is Ax) concave down if f "(x) = 3x' – 14x² + &r?

A: Given that, f''x=3x3-14x2+8x For what value of x is fx concave down.

Q: If f'(x) > 3 for all x and f(2) = 5, what can you conclude about f(4)? %3D

A:

Q: If you need to prove that a ∈ f^−1 (Y ), what do you need to show?

A: Here we need to show the way to prove a∈f-1(Y)

Q: The ratio of f(x) to g(x) is 3: x+2. If f(x)=x-2, what is g(x) in terms of x?

A: we have given ratio of f(x) to g(x) is 3: x+2 and  f(x)=x-2

Q: Let f(x) = x3+ x +4 and g(x) = 2x + 3 in Z3[x]. Then, upon dividing f(x) by g(x), we get The…

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Q: Given f(x)= x^3 − 6x^2+9x, find the multiplicity of the zero at x = 3

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Q: Express f(x) in the form f(x) = (x- k)q(x) +r for the given value of k. f(x) = x° + 6x2 + 10x + 4,…

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Q: Given that f(x) = kx° + 2x2 + 3x + 6, find k such that if f(x) is divided by (x- 2), the remainder…

A: Answer written in image with explanation.

Q: Find a general formula for f("(x) if f(x) = 11x²e*. pln)(x) %D

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Q: Find the quotient and the remainder upon dividing f(x) = 2x°+4x*+3x+1 by g(x) = 3x+1 in Z„[X].

A:

Q: If f(3) = 11 and f '(x) ≥ 1 for 3 ≤ x ≤ 6, how small can f(6) possibly be?

A: Given,          f3=11 and f'x≥1 for 3≤x≤6.

Q: Given, F(x) = 2x+3/4x+5 for x ne-5/4; f^-1(x)

A:

Q: Let f(x) = x³ +x + 4 and g(x) = 3x + 2 in Zs[x). Then, upon dividing f(x) by g(x), we get None of…

A: Every integer polynomial we can write as an polynomial in Z5(x). Using this idea again and again we…

Q: The polynomial of degree 3,P(x), has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at…

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Q: Determine the error term of for the formula: f'(x)  ≈ (1/4h) [f(x+3h) - f(x-h)]

A: In order to find the error term of the given expression, first find the value of f(x+3h) and f(x-h).

Q: If f (x) = /In(x²) + x², what is the value of f'(1)? %3D

A:

Q: Given that f(x) = 3x²- 3cx +2, find c such that if f(x) is divided by (3x – 1), the remainder will…

A: Using synthetic division we have to find the value of 'c' for which the following function when…

Q: f f(x)=3^{ax}+3x and f'(0)=3, find the value of a using 2-points formula with h=0.5.

A: Introduction: The derivative of a function y=fx at a point x=a can be approximated as f'a≈fa+h-fah…

Q: Given R(x), find R(−2). R(x) =  3x + 11 −6x3 + 33x

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Q: Find k such that F(x)=x^3-kx^2+kx+44 has the factor x-4

A: To find k such that F(x)=x3-kx2+kx+44 has the factor x-4.

Q: If f(x) = 5x - 2, g (x) = – 2r + 3 and h (x)= x, then (fogoh)(-2)=.... %3D

A: The functions are f(x)=5x-2g(x)=-2x+3h(x)=x3 If f(x) and g(x) are two functions then the composition…

Q: Let f(x) = x + px + qx + 5 where p, q are constants. The remainder when f(x) is divided by (x + 1)…

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Q: Given an interval [a,b] that satisfies hypothesis of Rolle’s theorem for the functionf(x)=x4+x2−2.It…

A: Rolle's theorem states that "If a function f(x) is continuous on the closed interval [a, b] and…

Q: Given an interval [a,b] that satisfies hypothesis of Rolle’s theorem for the…

A: Given function is x3-2x2+3 .

Q: Let f(x) = x3 + x +4 and g(x) = 2x + 3 in z,[x]. Then, upon dividing f(x) by g(x), we get The…

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Q: 5) [ (x² +1)´dtan x3

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Q: If ƒ(x) = 3ªx + 3x and f'(0) = 3( by using 2-points fomula with h=0.5), then the value of a is

A: Topic- derivatives using 2 point formula

Q: Given f(x) = In(x) + 7x2 - 19r, find f'(3). %3D

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Q: The average pollen count in a certain city on day x of the pollen season is  P(x) = 8x − 0.2x2…

A: The average pollen count in a certain city on day x of the pollen season is  Differentiating with…

Q: Let f(x) = x³ + x +4 and g(x) = 2x + 3 in Zs[x]. Then, upon dividing f(x) by g(x), we get The…

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.