Suppose that the functions r and s are defined for all real numbers x as follows. r(x) = 6x s (x) = 2x+3 Write the expressions for (r+s)(x) and (r-s)(x) and evaluate (r s)(2). (++s)(x) = D %3D (-- s)(*) = [] %3D (r-s)(2) = D %3D

Q: Find critical number of f(x) = 5x^2-8x+1

A: Given,          fx=5x2-8x+1

Q: (b) Suppose that f(x) : УBx2 — 3 (Bx +2 if if x 2 Find the value of ß so that f(x) is continuous…

A:

Q: Prove that for integers y=1 the equation 3h-n (2x₁ + x₂ + 4x₂) +3² (~1(2x₁+x₂+.+xn-1)+...+3^-1 (2²₁)…

A: We will use contradiction to prove it.

Q: If the function f (x) is continuous for all real numbers and if f (x) x²-4 when x + -2, then x+2 f…

A: f(-2) = -4

Q: - Find f '(x). f(x) = - 3 In x+ 11x² - 9 f '(x) = . Find f '(x) f(x) = -9-5x + 4 ex f '(x) = . Find…

A: Solve for the derivative

Q: if 4x Suppose that g(x) = {ax + b xS-1 if - 1<x < 2 if x2 2 Find the value of a and b such that g(x)…

A:

Q: Let ƒ(x) = x3 - x - 1. Use the Intermediate Value Theorem to show that ƒ has a zero between -1 and…

A:

Q: Find a formula for f-(x) and (f-1)'(æ) if ƒ(x) = -V5 – x f-' (x) = (5-1)'(x) =

A:

Q: find critical numbers for f(x)=x4-4x2

A: Obtain the derivative of the function as follows.

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(0) = 0

A: Given: f(0)=0

Q: 29. For |x|<1, prove that 24x 1-x 16x 8x 1 + 1-x1+x ....... 8x &r = 1+ (1- x) (1 +x)2 ' (1-x)2 ...

A:

Q: Q\ Determine a condition on |x - 1| that will assure that * 1 |x² – 1| < |3

A: Given that |x2-1|&lt;13 That is -13&lt;(x2-1)&lt;13

Q: 5. Check the continuity of r+5| 2x+10 x + -5 f(x) = x = -5 at x = -5.

A:

Q: 0.2 Differentiate In x+1, with respect to x. x²-x+1

A:

Q: Find critical number of f(x) = x^2 - 6x + 8

A: To find critical number of f(x) = x^2 - 6x + 8

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: Find real zero of f(x) = x* – 2x³ – 4x² + 4x + 4 within TOL = 10-5 by following methods:

A: First, plot the curve for f(x). Use the graph to find a real zero as mentioned in the question.…

Q: If f(x) has odd degree and negative leading coefficient, as x goes to -∞, then f(x) would go to

A:

Q: how that the function  f(x)=x3-3x2+3x-100 is increasing on R

A:

Q: Find critical number of f(x)=x^3-6x^2

A: Given: f(x)=x3-6x2

Q: x -4x +5 - Prove that: f' x x-2

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 2 2x + 4 if x ≥ 2 on the open…

A:

Q: 17. Find the end behavior for f(x) = -3x - 2x -7 A. x- +o, f(x) +0 x -o, /(x) - - B. x-+o, /(x) -00…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: f(x) x* + 3x - 3x + 2 %3D as x -00 f (x) → 0 as x -of (x) → -∞ as x +∞f(x) → -∞ as x → +of(x) → +o

A: Given polynomial f(x) =-x4+3x2-3x+2

Q: Find Absolute Extremums of F(x)=2x^3-6x over [0,3]

A: To find the absolute extremums of the function F(x)=2x3-6x over [0,3]

Q: 2 Show that the function f(x) = x-4x + 10x has no relative extreme points. 3X Relative extreme…

A: Given, Function: f(x) = 23x3-4x2+10x Differentiate f(x) with respect to x, we get: f'(x) = df(x)dx…

Q: 2- Let g(x) = x5 - 8.6x* + 38.782x3 - 17.25x² - 4.5927x + 10.5 then the value of g(0.25 x 101) =…

A: The objective is to state whether the statement is true or false. For the polynomial…

Q: What is the smallest integer a where f(x)=2x is always greater than g(x)=x2 for all x>a?

A: Given  : f(x) = 2x is always greater than g(x)=x2 for all x &gt; a  Implise that :  2x &gt; x2

Q: A³ f2 = V³ fs 3

A:

Q: Suppose that 0 &lt;ƒ′(x) &lt; 1/2 for all x-values. Show that ƒ(-1) &lt; ƒ(1) &lt; 2 + ƒ(-1)

A: From the given inequality the behaviour of the function can be determined as.

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: 4. If the domain of f(x) is -35x59 and the range of f(x) is 25ys15, then which of the following…

A: Here we can use the concept of transformation of function as for given function f(x) the…

Q: If the leading coefficient of an odd-degree polynomial function is positive, then the function…

A:

Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

A:

Q: Find critical number of f(x) = x^2-7x+8

A: Given function f(x) = x2-7x+8 The critical number is the value of x which makes derivative of f(x)…

Q: Find (f 1)(a) for f(7)=0, f'(1)=-1, and a=0. -л -1 1/л -1/n

A: topic - derivative of inverse function

Q: (i) Show that f(x) = 6x³ – 2x2 + 4x – 3 has exactly one real root. (j) Show that f (r) = x + 2x5 +…

A: Given: i. fx=6x3-2x2+4x-3ii. fx=x7+2x5+3x3+14x+1 To Show: Given equation has exactly one real roots.…

Q: Use the intermediate value theorem to show that f(x) = 4x^3 - 6x^2 + 3x - 2 has a root between x = 1…

A:

Q: Find all zeros. f(x) = x^4−x^2−30 f(x) = x^4+ 2x^2−15 f(x) = 3x^3−7x^2−7x+ 3

A: Since you have sent more than 3 sub parts therefore according to our policies we are bound to answer…

Q: Find the critical number of f(x) = 3x^2 - 18x + 4

A:

Q: 2/3 of f(x) = (x²4)73. (b) Find all critical nurabers

A: There are multiple question. As per company policy kindly ask other question separately. b.

Q: Find critical number of f(x) = 4x^2 + 8x -1

A: We have to find critical number of  f(x) = 4x2 + 8x - 1 To find critical number, differentiate f(x)…

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(1) = 0

A: We have, f'x=2x Integrating both of the side with respect to x, we get the result as…

Q: - Find all critical numbers of f(x) = 3x* + 20x – 36x²

A:

Q: Find critical number of g(x) = x^2 - 8x +9

A:

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.