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

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: 2. If the area (A) of the rectangle is (4x³ + 5x + 7) and the width (W) is (x + (Z + 4)). Find the…

A:

Q: f(x)=x^3-18x^2+105x-197 For what numbers does ff have a critical number?

A: To find the critical number of a function f(x) , set  f '(x)=0 and then solve for x.

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: 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*…

A:

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

A:

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

A: We can solve this problem using partial derivatives.

Q: For the function y=4sin(2(x-3pi/4))+1, match the following:

A:

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: Suppose that x and y are real numbers such that y is 6 greater than x. What is the smallest possible…

A:

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: 2. GIVEN: f)=3x²2x+5 AND FIND: a) flxth)-f() %3D

A: The given functions,f(x)=3x2-2x+5 and g(x)=4-x

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: The funetion fCx) =ax3+bx?+|16X+3 as a factor, when the function dlivided bu (x+l) the nemainder i…

A:

Q: 1 Given that x 2 Vx, express 4* + 4* as a single power of 4.

A: We have to express 4x + 4x as a single power of 4.

Q: 15.f mOT-(27+ 3)', mRT- (9x – 5)" and MRST - (10x-2), find mi.

A: Given,         QT⏜=27x+3° , RT⏜=9x-5° and ∠RST=10x-2° .

Q: Given that f(x) = 3x – 1, g(x) = 2x and h(x) = x + 1, determine: a. hgf(x)  b. hgf(-2

A: Given : f(x) = 3x-1             g(x) = 2x             h(x) = x+1  To Find : hgf(x)…

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: Determine the constants a and b so that x = -1 is a zero point to q (x) = x5-3bx3 + ax2-ax + b with…

A:

Q: For the function f(x,.y,2) In (8x2 -7y4 +2xz2), find f, fy, fz, and fz

A:

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

A:

Q: from the first principle defferentiate h() = 5x³²x+7 2² +2+1

A:

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: Find the constant C such that .4 x3 - 3x + 5 < C,

A: x3 - 3 x + 5≤c x∈{0,3}

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…

A:

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: Suppose we want to form an interpolant at equally spaced points xo = 0, x1 = h, and x2 = 2h of the…

A:

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

A:

Q: find the value of k so that the remainder is R when f(x) is divided by (x – r):   f(x) = 2x2 + 3kx…

A: Since, you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Suppose XY is congruent to YZ. If XY is 8x + 8 and YZ = 2x + 18 what is the value of x? If needed,…

A:

Q: 2. If x =-1 and z = 2y = -3x, find the value of 3xy-z 1+3x²z

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: What value of x woula prove (8x- 31) (5y+ 35) (6x +3) m

A: The value of x is:

Q: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=5 and a root of multiplicity 11…

A:

Q: DETERMINE THE ROOTS OF THE EQUATION USING: REGULA FALSI METHOD f(x) = x³ – 3x + 1 Using a…

A: To determine the roots using Regular Falsi Method.

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

A:

Q: 4. For f(x) = 3x² + 5 and g(x)=7x-2, %3D %3D

A: answer is in next step

Q: on f(x, y) = 7x2 + 9y? - xy + x.

A: Let the function be, f(x,y)=7x2+9y2-xy+x. Differentiate the function partially with respect to x.…

Q: Show that for r=1x1 XER³, > A( 7 ) = 0 we have when 1x1=1 #0

A: Laplacian operator

Q: 2). when 2x°-3x+Kx-1 is divided by X-1 the remainder is 2, find Ke

A: value of k is 4  see below the calculation and answer

Q: 5) [ (x² +1)´dtan x3

A:

Q: By applying product rule to find y' 3 (1+x*) x4 - x*

A:

Q: The number of units in Z29[x] is

A: Solution by using definition of unit elements

Q: Use cubic interpolation method with two points to find µ2 , where a = 0.6, h = 0. 1, ɛ = 0. 001 and…

A: Given: Let's determine μ2 using cubic interpolation method,  here a=0.6, h=0.1, ε=0.001,ϕι=-2.7

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

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.