For what value of the constant c is the function f continuous on (-∞, 0)? cx? + 2x if x < 3 f(x) = { if x 2 3 - CX C =

Q: 1) Find the absolute extremum values of f(x) = x² - 3x + 12 over the interval 1, 3]. -

A: The extreme value of function at f(3)= 30

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 20 over the interval [1, 3]. [2 - marks]

A: We have to find the absolute extremum values of the given function.

Q: The value of (x,f(x)) for the upper and lower limits of the function fx=x^3-6x^2+4x+8 and for the…

A: Given function is fx=x3-6x2+4x+8find the upper and lower limits of the function for the period…

Q: In the function:  f(x)=(12−3x)e^x  What are the critical numbers of the function?  When is the…

A:

Q: Find the critical numbers of the function. f(x) = x² log,(x? + 2)

A: fx=x2log7x2+2⇒fx=x2logx2+2ln7      ∵logab=logblna Critical numbers are the values of x for which…

Q: e^x=3-2x

A: Given; ex=3-2x,(0,1)

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 20 over the interval [1, 3].

A:

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 16 over the interval [1, 4].

A:

Q: 1) Find the value of C that make the function continuous at x-1? x 1 -

A: We have given piecewise function  Function is continuous at x=1 if  f1+=f1=f1- f(x) = C-x        if…

Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x² – 4…

A: f(x)=x2-4x-2x&lt;2ax2-bx+32≤x&lt;32x-a+bx≥3

Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

A:

Q: 7. Find the absolute maximum and absolute minimum values of f(z) = 2x – 3r2/3 on the interval…

A:

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: Find the critical points and the intervals on which the function f(x) = (x³ – 2x) e* + 4 is…

A: Consider the function and find the derivative of the function and critical points.

Q: 18. Solve for A and B so that f(x) has a limit at both x = 2 and x = 4. 3x + 4, x> 4 f(x) Ах + B,…

A:

Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: 7. For what value of the constants A and B is the function f continuous on (-0o, 0)E AV-x+6-1 for x…

A:

Q: if x < 6 cx2 + 7x x3 - cx Let f(x) = if x 2 6. For what value of the constant c is the function f…

A:

Q: If G(x,y) is differentiable with respect to x and y then it is always possible to find the number…

A:

Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

A:

Q: If f(x)= (x^4) + 3x + 1 and there are two roots x=a and x=b in the interval [-3,-1] with a &lt;b.…

A: The given function is,

Q: Find the linearization of f(x)=ln(x2-3) at suitably chosen integer near X=2.1. Then use the…

A:

Q: -2 x< -1 Q1)a) For what values of a and b is g(x) = ах — b -1<x<1, x21 Continuous at x= -1

A: The suitable formula for continious       LEFT HAND LIMIT = RIGHT HAND LIMIT

Q: 8. If f(x) = 4 sin x + 6 and g(x) = 3x + 5, what is the maximum value of f(g(x))?

A: Solution is given below

Q: For what value of the constant c is the function f continuous on the interval (-0,00). f(x)={ cx+1 ,…

A:

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: For all but two choices of a, the function (x) x if x a will be discontinuous at the point x = a.…

A:

Q: For what value of the constant c is the function f continuous on (-∞, +∞)? cz +4 if x ≤ 10 f(x) =…

A:

Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 12 over the interval [1,3]. [2 marks] %3D -

A: Given: fx=x2-3x+12 over the interval 1,3

Q: 2. Find the values of the constants a and b for whichf is continuous everywhere if ax + b, f(x) =…

A:

Q: 19. Solve for A and B so that g(x) has a limit at both x = -1 and x = 3. 4x - 2, X> 3 g(x) Ax + Bx +…

A: To solve for A and B so that gx has a limit at both x=-1 and x=3. gx=4x-2,       x≥3Ax2+Bx+2,…

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 When is the function concave up and concave down in…

A: For concavity we need second derivative.

Q: For what value of the constant a is the function continuous on (-0, 0). for r 1 f(x) ax a =

A:

Q: 6- if f(x) is a continuous function at x = 0, then a = 1- cos 4x x0 V16+ Vx -4 3.

A:

Q: A continuous function y f(x) is known to be negative at x = 2 and positive at x=7. Why does the…

A: Given that f(x) is a continuous function.

Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…

Q: Find the critical points and the intervals on which the function f(x) = (x³ – 4x) e* + 15 is…

A: given f(x)=x3-3247xex +15 we have to find the critical points and the intervals on which the given…

Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b -1<x<1, 3 x21 Continuous at x=0

A: F is continuous at any point then left hand limit is equal to right hand limit. if limit is not…

Q: The Second Derivative Test cannot be used to conclude that x = 2 is the location of a relative…

A: We need to check for which of the given functions, can't conclude about location of  a relative…

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 constants A and B such that the function x2 f(x) = if x 2 is differentiable at x = 2.

A:

Q: (b) Show that f(x) = ln(x + 2) has a unique fixed point in [0, 2].

A:

Q: *show work*

A: Given:A continuous function y = f (x) is known to be negative at x = 4 and positive at x = 9.

Q: 1. f(x) = x2 + x – 1 for all values of x %3D

A: A detailed solution is given below

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 8 over the interval [1, 4].

A: f(x) = x2 – 4x + 8

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.