Find the value of k so that the function defined by f(x) =kr - 15 S2² + 25 x < 5 is continuous at a = 5. x > 5 |-

Q: The function f(x) = 3x³ + cos(3ræ) + 2x , x > 1 is known to be a strictly increasing function on its…

A: Given f(x) = 3x3 + cos(3πx) + 2x,  x≥1   ⇒ f'(x) = 9x2 - 3πsin(3πx) + 2

Q: The function F(x) : te dt is cocave down for all x > 0.

A: Proceed as shown below...

Q: If f(x) = ∫0 x   (1 - t^2)e^t^2 dt , on what interval is f increasing?

A: To determine the interval on which f is increasing. f(x)=∫0x(1-t2)et2dt

Q: 9. Find the value(s) of k that makes the function continuous over the given interval. fx) = {3x + 4,…

A: Solve the question number 9 as asked by the user

Q: Determine the interval(s) where f(x) = is continuous. 1- In(1/r)

A: It is given that, f(x)=11-ln1/x   A function is said to continuous in an interval in which it is…

Q: Given the function h (x) = : x+1 Over what interval(s) is h (x) decreasing?

A:

Q: (a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

A: Consider the given piecewise function

Q: 8. Suppose that f is a continuous function such that f'(x) > 0 for all æ, f(0) = 0, and f(1) = 1. If…

A: f'(x)&gt;0 for all x, f(0)=0 and f(1)=1.To Find: If ∫01f(x)dx=13, find the value of ∫01f-1(x)dx.

Q: Find the value(s) of k that makes the function continuous over the given interval. 0 sx s2 2 < x s…

A:

Q: 54. Is the function given by SEx + 4, for x s 3, 2x – 1, for x > 3, g(x) continuous at x = 3? Why or…

A: The given function is;  g(x)=13x+4for x≤32x-1, x&gt;3 we have to check the given function is…

Q: Find the absolution extrema of f(x) = (In x)2 on [1, e].

A: We have to determine absolute extrema of girls question

Q: 1. Given the function 2r + 1, r 1 Verify whether or not the function f is continuous at r 1.

A: the given function is: fx=2x+1,     x≤14x2-1,       x&gt;1 we have to verify whether or not the…

Q: The function f(x) = x + 1/x is O Decreasing on (0,1) O Increasing on (0,1) O Increasing on (-1, 0) O…

A: Answer is written below

Q: The function f(x) = 2 + 1/x is continuous on the following interval EXCEPT. O a. [-2,-1] O b. [1,2]…

A: At any point a for a function f(x) the limit limx→afx=L exists if the limx→a−fx=limx→a+fx=fa.

Q: State the interval(s) over which the function f(x) = V16 – x² is continuous.

A: Given, fx = 16-x2   We have to state the interval over which the function is continuous.

Q: For what values of a is the following function continuous for all x? Show the work. a²x +4a if x >…

A: See the attachment.

Q: For what value of k is the function f continuous on (-o0, 00)? z – 1 ka² – a + 23 if a > -4 if z <…

A:

Q: 45. For what value of a is x2 - 1, x < 3 2ax, f(x) = %3D 2ах, continuous at every x?

A:

Q: Find the value(s) of k that makes the function continuous over the given interval. a < k k < a S 3x…

A:

Q: The function f(x) = x + 1/x is %3D O Decreasing on (0,1) O Increasing on (0,1) O Increasing on (-1,…

A: In this question we are given with the function and we have to find the graph of the function is…

Q: Find the x-value corresponding to the absolute minimum value of f on the given interval. (If an…

A:

Q: If we use Simpson's rule for a function f(x) = X +1 with n=4 , then the approximate of S f(x)dx is

A:

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A: Given,          fx=1x+lnx ; 0.4≤x≤9

Q: Consider the graph of a function f shown below. How many critical numbers does f have on the…

A:

Q: Sx+2, if x 1 Value of k that will make f(x) continuous on (-0, 00) is ....

A: K=3 makes f(x) continuous.

Q: Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0…

A:

Q: 3. Find the value of k that will make f continuous on (-o, 00). NORS x + 19 if x 1

A:

Q: 55. Let F be a function given by Sx2 + 1, for x s 2, 2x + 1, for x >2. F(x) = a) Verify that F is…

A: We have Fx=x2+1 ,  for x≤22x+1 , for x&gt;2 We have to verify   (a) Function is continuous at x=2…

Q: Compute G' (x), G" (x), and deduce the intervals of increase or decrease of G, its local extrema (if…

A:

Q: The function f(x)=³ in (x) is continuous everywhere except x (х-1) at x=0 and at x=1. When…

A:

Q: Find the values of c that make f continuous everywhere: ´x² – c² if a 9 smaller c = larger c = Use…

A:

Q: Find the value of a such that the function S(«) = {** -1, x < 3 x 2 3 | f(x) = 2ах, is continuous at…

A: Given:      f(x) = x2 - 1  , x &lt; 3     f(x) = 2ax  ,   x ≥ 3

Q: Find values of the constants k and m, if possible, that will make the function f continuous…

A: If f is continuous at x=a then limx→a-fx=limx→a+fx=fa . Assume , f is continuous every where to find…

Q: H.W Ex 2: Determine if the f(x) is continuous at x 3 ? at x-3 f(x) =- x²+2 at x 3

A: Given query is to find f(x) is continuous or not at x = 3.

Q: The function f(x) = x + 1/x is 2p O Decreasing on (0,1) O Increasing on (0,1) O Increasing on (-1,…

A:

Q: 4) Find the value of the constant k so that the function (1 – k, if z<3, f(z) = 1– kr, if 123, is…

A: This question is related to limit and continuity of a function, we will use condition for a function…

Q: Determine if the function f below is continuous at x = 1: ſ1– VT- x, x 1

A: According to question,given function,fx = 1-1-xx≤1ln xx&gt;1

Q: Find the values of a and b such that the following function a² cos(x − 2) — 26(³-x), if x 2, is…

A: Topic = Limits

Q: Find the constant a such that this function g(x) is continuous on the entire number line.

A: Given,

Q: 18. Consider the function f (x) 5e2r. On what interval(s) is f (x) %3D increasing? On what…

A:

Q: Find the values of α and β such that the function f(x) =αcosx + 2 if x < 0  and f(x) = βe3x + αx2…

A:

Q: 3. Find the absolute extrema of the following function on the indicated interval. f(x) = x3 – 3x on…

A:

Q: 4. `s.] Find the number a and b at which f is continuous everywhere? x² -1 if x 2

A:

Q: 7. Suppose that the function f (x)=2-sin(e*) is continuous on with equal step 2'2 size, h equal to .…

A:

Q: a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

A:

Q: function, that is 0 everywhere except at t=0, is know as:

A:

Q: Give a formula for f(x) given that f is continuous and 2 x +x* + 2 = f (t) dt t+ 2

A:

Q: Find a value of k making h(x) continuous on (0, 5). 0 < x < 2 2 < x < 5 h(x) = x +1,

A: A function is continuous if limx→a+ h(x)  = limx→a- h(x) = h(a) Now in the given question, function…

Q: Find the value k that makes the function continuous. S ka?, f (æ) = x > 2 ka + 4, г 2

A: Given thatfx=kx2         x&gt;2kx+4    x≤2We have to find value of K for which function is…