2, f(x) = x < -1 ах + b, — 1

Q: The function f(x) =3 x4-4 x3-12 x2+1, is increasing on the interval

A: f(x) = 3x4-4x3-12x2+1f'(x) = 12x3-12x2-24xf'(x) = 12x(x2-x-2)f'(x) = 12x(x2-2x+x-2)f'(x) =…

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

A:

Q: 11. Find the absolute extremum of f (x) = 4- x3, where -2 < x< 1

A: Given: The function is  f(x)=4-x3,  -2≤x≤1   To determine: The absolute extremum of the function…

Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): x² 4 x -2 f(x) = { mx² 2 m = n =…

A:

Q: Confirm if the Mean Value Theorem applies to the function f(x) = v25 – x2 on the interval [-3,4] and…

A:

Q: For which interval is the function f(x)=x√√4-x² continuous O (-∞, -4] and [4, ∞) O (-∞, -2] and [2,…

A:

Q: For what value of the constant c is the function f continuous on the interval (-,00). Sa? – 3, x с…

A:

Q: For finding the root of the function: f(x) = 3x – x² Do 2 steps of the bracketing method, given the…

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on…

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 constant a such that the function is continuous on the entire real line. Ax) = {2x2, (ах -…

A: Given that , the functionfx=2x2,x≥1ax-7,x&lt;1We have to find constant a such that the function is…

Q: For what value of k will the function f be continuous on (-∞, 0)? { x2 – 16 if x + -4 f(x) = x + 4 k…

A: We have to find

Q: For f(x)=3|x| does the Mean Value Theorem apply on the interval [-2, 2] and why?

A:

Q: Find numbers a and b, or k, so that f is continuous at every point. 5) f(x) = 10x + 8,if x < -1 kx…

A: If f is continuous , solimx→-1-fx=limx→-1+fx

Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: Determine the absolute extreme values of f(x) = 5x – 10~/x on the interval [0, 16].

A:

Q: Find all possible (real number) values of p, q, and r, if any, which result in the following…

A:

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

A:

Q: Let f(x)=-4cosx and g(x)=2cosx+3 for 0&lt;x&lt;2pi solve for f(x)&gt;(g(x) on [0,2pi]. Write the…

A: Sketch the graph of -4cosx&gt;2cosx+3 .

Q: 3. f(x) = v2x – 5 at x = 3 -

A: (3) Given function is fx=2x−5 We have check whether the function fx is continuous or not at x=3 For…

Q: For what values of a, m and b does the function x = 0 0 < x < 1 1< x< 2 3, f(x) = -x² +3x + a, тх +…

A: to find the values

Q: 2) State the intervals of concavity in the function f (x) = x3 + 2x2 – 4x + 5.

A: We have to determine the intervals for concavity of the function: fx=x3+2x2-4x+5 To check the…

Q: (c) For what values of a and b does the function ах 3, x < 4 f(x) = (-x² + 10x – b, x 2 4 satisfies…

A: Answer:   a = 0 and b = 27

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

A:

Q: For the function, find the number in the given interval which satisfies the conclusion of the Mean…

A:

Q: (c) For what values of a and b does the function (ах— 3, x 4 satisfies the conditions of the…

A: Function  To find the values of a and b for which f(x) satisfies the conditions of the Mean-Value…

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

A:

Q: (c) For what values of a and b does the function ах — 3, x < 4 f(x) = (-x² + 10x – b, x2 4 satisfies…

A:

Q: 4. Find the intervals in which the function f(x) =x³ – 6x2 +9x +30 is concave up/concave down. Also…

A:

Q: 2, C. Find the value for a and b such that f(x) = {ax + b, if-1 <x<3 is continuous for all (-2, if x…

A: Given that fx=2if x≥1ax+bif 1&lt;x&lt;3-2x≥3is continuous for all real numbers. The objective is to…

Q: 3- Find the root of function F(x) = x² – 10 Using XL=3 , X,-4 , ɛ = 0.1

A: given function Fx=x2-10 with condition XL=3, Xu=4, εS=0.1 claim- find the roots of the function

Q: Find the value for k so that the function will be continuous at x = 1. - 5x2 - 30x + 35 - 10 if x <…

A:

Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+2, f(x) = { ax³, (x² +…

A: Given that f is a continuous function, then it is continuous at all the point. So, the function is…

Q: Find the absolute max and min values at the indicated interval  f(x)=2x^3-x^2-4x+10 ;[-1,0]

A: Absolute maximum and absolute minimum values of a function exist at a point where its first…

Q: Given the function of f(x) = -3 – in the interval [-8, –2], find a point x = c between -8 and -2 so…

A:

Q: Find the constant a such that the function is continuous on the entire real line. (8x?, lax – 6, x2…

A: Given function f(x) = 8x2-x≥1ax-6, x&lt;4we find constant 'a' such that the function is continuous…

Q: (2) For the function f(x)=--x² – 24x +19 3 (i) Determine the turning points and the values of the…

A: Answer is following.

Q: Prove that the functionsf(x)=√x2+4x+3 and g(x)=x3+2x2 / x2+1are asymptotically equal to each other…

A:

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: Find the values of a and b that make f(x) continuous for all real numbers. (x+ 2, f(x) = { ax³, (x²…

A: f(x)=x+2,x≤-1ax3,-1&lt;x≤1x2+bx,x&gt;1

Q: Over which interval is the function f (x) = x3 -4x2 + 5x concave upward?

A:

Q: Find a and b so that the function = { ax + b, 8x – 8x? + 4, ах + b, х -2 is both continuous and…

A: Continuity at x=-28-23-8-22+4=a-2+b-64-32+4=-2a+b-92=-2a+b→1

Q: Find the constant a such that the function is continuous on the entire real line. (9x², Flx) = {9x?,…

A: Given function is : fx=9x2    ,      x≥1ax-6   ,    x&lt;1 Here given that function is continuous…

Q: Find the constant a such that the function is continuous on the entire real line. 5x², ах — 7, f(x)…

A: For a function to be continuous, the value of the left and right limits at critical point needs to…

Q: Find the open intervals on which the function is increasing y = x/100 – x²

A: A function is said to be increasing in an interval its derivative is positive in that interval.

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: For the function f(x)= (8+2x, if x5) A) use definition of continuity at a number (3- step test) B)…

A: Concept: These are the three requirements for continuity: 1). The equation for the function is x =…

Q: Find and classify the extreme values of f(x)= 6x* –4x° over the interval [-2,2].

A: Given,  f(x)=6x4-4x6

Q: 7+6z – zº x 4 тх + b,

A: Given that,    A function is continuous everywhere means the function is continuous at every point…

Q: Lars was 20 inches tall when he was born, and six foot one when he died at age 83. Use the…

A: Intermediate value theorem :- Let f be a continuous function on [a,b] and f(a) =/ f(b) with f(x)…

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.