Sx³, x < 2 f(x) lax?, х > 2 x²,

Q: Find the open intervals on which the function is increasing or decreasing            f(x) = x2 + 3x…

A: We find f'(x) using the power rule

Q: Find the value of k that makes the function continuous. Justify your answer. 2x – 1, x 2

A:

Q: Find numbers a and b, or k, so that f is continuous at every point. 3x+ 9, if x<-6 f(x) = { kx+ 6,…

A: Hair we are given that the function is continuous at every point. we use the concept of limit for…

Q: Find the absolute extreme values of the function on the interval. F(x) = Vx, -27sxs8

A: We will first differentiate the function to find the critical points.

Q: Find all absolute maxima and minima values for the function y=x^2+(54/x), on the intervial [1,108]

A:

Q: Find the absolute extrema of the function on the closed interval.

A: Find the derivative for g(x).…

Q: Find the range and domain of the function, f(x,y) = sqaure root of (36-x2-y2)

A: Given function is f(x,y)=36-x2-y2We have to find the domain and range of…

Q: Find a and b so that the function 1 5x3 — 6х? + 3, х -2 f(x) = ах + b, is both continuous and…

A:

Q: Find the constant a such that the function is continuous on the entire real line. (x) = {4x?, ах —…

A: We have to find a

Q: For what value of the constant c is the function continuous on all real number? f(x)={c°x² -4cx…

A:

Q: -pose f(x) = (x² – 9)2/3. Find the intervals rvals on which it is decreasing.

A:

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x <0…

A: For a function to be continuous at x = a, it must satisfy the following condition:

Q: •On what intervals) is the function y=-4x*+ (6x"n both increasing and cocave down?

A: Given,  The function  y = -4x2+6x17     We have to find the intervals in which function is both…

Q: Given the function f(x) =4x³– 39x²+90x +2, which of the following describes its absolute extrema at…

A: Given that, The function is following, f(x) = 4x3 - 39x2 + 90x + 2 We have to find the absolute…

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

A:

Q: Find the constant a such that the function is continuous on the entire real line. 9x², ax - 3, a = x…

A:

Q: For what value of x does the function f(x) = x³ – 3x? attain the absolute maximum in the interval…

A: We have to find Absolute Maximum in the interval [-1,4] by Second Derivative Test.

Q: Find the open intervals on which the function f(x)=x+6*sqrt(5−x) is increasing or decreasing.

A: Given, f(x)=x+65-x

Q: The function f(r) = x - 18x2 is increasing on the intervals

A:

Q: 4x 82. f(x) = X - 3

A:

Q: Find the constant a such that the function is continuous on the entire real line. 8sin x if x < 0…

A: For continuity of f(x) LHL=RHL     so find lhl and rhl and equate both to get a.

Q: Find the constant a such that the function is continuous on the entire real line. 1 = √7x², lax - 5,…

A: Topic = Function

Q: Find the domain of the function. h(x) = Inx+In(2-x). Express your answer in interval notation.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the constant a such that the function is continuous on the entire real line. 8sin x If x < 0 if…

A:

Q: Locate the absolute extrema of the function on the closed interval [-60,60]

A:

Q: Determine where f(x) is continuous, algebraically. Enter the answer in interval notation.

A: Given data: The expression for the given function is f(x)=log18(10x+150)-7x. The given function is…

Q: The absolute maximum of the function f(x) = 2x? – 13x + 9 over 1, 6]. -

A:

Q: Find the absolute extremum value 1. f(x) = x - 8x² + 16; on [-3,1]

A: Introduction: The maximum and smallest values of a function within a certain set of ranges are known…

Q: Find the area in the first quadrant, bunded by the function, f (x) = 3/x+1 , and x = 4

A:

Q: Find the domain of the function h(t)= 4/t write in interval notation

A: Domain of a function is the set of points on which function is defined. here, we have to find the…

Q: Find the absolute extrema of the function on the closed interval. F(x) = x³ -?, (-1, 4] 2

A: Given,            fx=x3-32x2 , -1,4To find : Find the absolute extrema of the function on the closed…

Q: Find the open interval(s) on which f(x) = - 5x+ 50x +8 is increasing or decreasing.

A: Given that:

Q: On which interval is f(x) = x³ – 12x + 12 decreasing? ㅇ (-8;2) ㅇ (-8, +8) | O (-2,+0) O (-2, 2) O…

A:

Q: 3. Given f (x) = 5x² and g(x) = Vx – 3 , what is the domain of (f • g)(x)? Write your answer in…

A: f(x)=5x2, g(x)=x-3

Q: The absolute maximum of the function f(x) = 4x? – 13x + 9 over [1, 5]. -

A: Given, f(x)=4x2-13x+9   over  1,5 To find: Absolute Maximum of f(x)

Q: Q2: Verify by the Mean-Value theorem and find the constant C in the interval [0, 2] in f(x) = 2x3

A: We have to verify and find the value of c

Q: Use (f(a+h)-f(a))/h to find and solve f(x)=2x^3-x^2+1

A: The given function Use the formula

Q: Given the function k (x) = 2x³ – 9x² + 12x + 9. Find the interval when k (x) is concave upward.…

A:

Q: Next, use the vertex and the other point provided to find the value of the leading coefficient a in…

A: Given that vertex is at -3,5, thus, h,k=-3,5.

Q: Q1: Find the extreme values of the function F(x,y)-x2 + п + у? +7 n=( 2x)

A:

Q: Find the absolute extrema of the function g(x) = -10x/x^2+9 on the interval (-5,2)

A:

Q: Find the differnce quotient with steps  use the function f(x)= x^2-16 and using formula…

A: Given that f(x)=x^2-16 differnce quotient f(x+h)-f(x)/h

Q: Find the constant a such that the function is continuous on the entire real number line. Sx³, x 2…

A: Given : f(x) = x3,x≤2ax2,x&gt;2 and the function is continuous. To find : value of a?

Q: Find the absolute extrema of the function f(x) = x³ 23-a on the interval

A:

Q: On which interval is f(x) = x – 12x + 12 decreasing? o (-2, 2) o (-00, 2) o (-0, -2) U (2, +0) ㅇ…

A: Let's find.

Q: -3 f(x) = x2 +2

A: By Absolute extremum value of a function f(x) we mean that the maximum or minimum values of f(x) for…

Q: Given the function f (x) = 10 + 5x³ – 3x³, identify the interval(s) where the function is concave…

A: Given:      f(x) = 10 + 5x3 - 3x5

Q: Approximate the zero of f(x) = x' - x + 3 in [-2, -1] to within 0.00001. Show your work!!!

A:

Q: B2. For the function f(x) = 2x³ – 18x?, determine the intervals where f is increasing and…

A:

Q: Find the domain of the function. (Enter your answer using interval notation.) k(x) =, Vx+4 x - 2

A: Given function k(x) = x+4x-2TO find : Domain of the function

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.