43) For f(x) a) Give the domain of f b) Evaluate (-2), (0) and /(3) c) Graphf d) Is f continuous on its domain?

Q: Show that f(2) =

A: We will show that derivative does not exist using definition. Then we will use geometry.  Calculate…

Q: What three conditions must be met for a function ƒ to be continuous at the point (a, b)?

A: Continuity at points: The points of continuity are the points where a function exist and has some…

Q: 3)Verify Rolle's Theorem for the function f(x) = 2x2 + 4 defined over the interval [-6, 6]. Justify…

A: Rolle's theorem is satisfied if : f(x) is continous at given interval. f(x) is differentiable at…

Q: What are the zeros of f(x)=2cos(3x)+1 on the interval [0,π]?

A: We have the given function as fx=2cos3x+1. In order to find the zeros of the function fx, we must…

Q: 4. Use limits to determine the values of a and b that guarantee the function below is continuous.…

A:

Q: Show that the functi on When x g 0 f(x)= +1 0 . When x = 0 is discontinuous at x = 0.

A:

Q: 67. Is the function given by g(x) 1 continuous over %3D x + 5 the interval (-4, 4)? Why or why not?

A: g(x)=1x+5

Q: What are the domain and range of g(x) = 3√x+4? OD: [3,) and R: [0, ∞) OD: [4,) and R: (-∞, 0) OD:…

A: The given function is: g(x)=3x+4

Q: Show that the absolute-value function y = abs(x) = |x| is NOT differentiable at x = 0. (Hint: by…

A:

Q: 19. Show that f(x) = x² + 1 is not one-to-one, using values of f (not the horizontal line test).

A: To show: The function fx=x2+1 is not one to one. Concept used: The function is one to one is and…

Q: Use the Trapezoidal Rule with n-6 to approximate. f(x)=sim2x.a=0,b=π

A:

Q: Explain why the function f(x)=cos.x-xmust have at least one zero on the interval [0,5]

A:

Q: explain the mathemahcal definition of continuily at x=3. Use sentences or math expressions in…

A:

Q: (b) Verify Mean Value Theorem for f(x)= 3x² – 7x – 4 over the interval[–1,4] .

A: Given: fx=3x2-7x-4

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: 6. State the (ɛ, 8)-Definition for continuity of a function f : R → R at x E R.

A:

Q: ,for x 1 Discuss the contuniuty of f andf'.

A:

Q: Let f be the function defined byf (z) = 3z2 -z. What is the absolute minimum value of f on the…

A: Topic = Application of Derivative  The absolute minimum value of f is 0.

Q: What is the function f on (a, b) if for all x1, X2 in (a, b) when x, f(x2). is it decreasing or…

A: for all x1 , x2 in a,b when x1<x2 then fx1>fx2 claim- is it decreasing or increasing

Q: 64. Is the function given by f(x) = continuous %3D =2- 6x + 8 at x = 3? Why or why not?

A: We have to check the given function fx=1x2-6x+8 is continuous at x=3 or not. To check the continuity…

Q: fully continuous for all x E R by use of the product rule differentiate the function f{x} = x3e-4x

A:

Q: and the domain of the function using interval notation. To enter ∞o, type infinity. To enter U, type…

A: We can solve this as follows:

Q: Draw the y = sinx and y = 1- x² on the domain -2 <x<2 and filling the between the funtions.

A: the filling part is given below-

Q: Let f(x) = /90 – x and g(x) Then the domain of fogis equal to a, b for = x? r. %3D - - and %3D

A:

Q: What is the continuous extension of f(x) = x3-1 at point x-1. %3D x2-1'

A:

Q: Find all values of a and b that make -а - х, x<-2 f(x) = {bx? + 1, Vx+b, -2<x<1 x21 continuous…

A: The function is given by: f(x)= -a-x , x&lt;-2           bx2+1 , -2≤x&lt;1         x+b   , x≥1 Also…

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: (b) Verify mean value theorem for f(x)=x² - 5x+6 over the interval [1,3].

A:

Q: Find the domain of f (x) = V3-x x(x+2) Use interval notation, "ninf" for -∞, "inf" for oo, and "U"…

A: Given: fx=3-xxx+2   The domain is the set of all x values at which function is defined and real.…

Q: The domain of f' is 1 (Type your answer in interval notation.)

A:

Q: Sketch the graph of a continuous function on [0, 2] forwhich the Trapezoidal Rule with n = 2 is more…

A: The midpoint rule is a method of finding the area under a curve. We use the midpoint of each…

Q: 3-The function f defined by 2. Is f is Continuous at x=| ?

A:

Q: Find the largest open interval using the tools of calculus where the function is changing as…

A:

Q: Does the Mean Value Theorem apply to f(x) = |x – 7| on the interval [1, 9]? Explain.

A: No

Q: 24. Is the function continuous on the interval (-5, 5] ? 3х-1 f(x) = x-4

A:

Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: Suppose f'(x) < 2 for all x 2 2, and f (2) = 7. Show that f(4) < 11.

A: Given that f'x &lt;2 for all x≥2 and f2=7.We need to show that f4&lt;11.

Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

A:

Q: 4. Verify Mean Value Theorem for the function f(x) = 2x ° - 6x2 + 2 in the interval %3D [a, b],…

A: given function :

Q: What is the lower limit and upper limit bounded by the curves y 9 - r2 and the line y = x + 7 ? -2…

A:

Q: Verify Mean Value Theorem for the function f(x) = x in interval [0, 9] %3D

A:

Q: Determine where f(x): V4 - x2 is continuous. Express the answer in interval notation.

A:

Q: 9. Discuss the continuity of the function x 2 x2,

A:

Q: What is the limit of f(x) = x^2 as x approaches infinity?* O Infinity Negative Infinity

A:

Q: Let f be the function given by ƒ(z)=2z + 3z² +1. What is the absolute maximum value of f on the…

A:

Q: By the definition show that f(x) = 2 + |x| is a continuous graph at the origin. Also, show the…

A: