a. Graph the function -1 < x < 0 x, f(x) = 0 < x < /4. tan x, b. Is f continuous at x = 0? c. Is f differentiable at x = 0? Give reasons for your answers.

Q: 1/x tan TC + x f(x)= .For what value of k, f (x) is k, continuous at x 0?

A: Introduction :We have given a function f(x) we have asked to calculate the value of k , if f(x) is…

Q: find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

A: Given: f(x)=tanπx2

Q: Apply Rolle's theorem to the following functions on given interval

A: Consider the function fx=x2-2x-3x+2, -1,3 Here, the objective is to find c such that -1&lt;c&lt;3…

Q: At what points are the functions continuous? x + 2 y = cos x

A: Consider the function: y=x+2cos x. Find the points of continuity. The function of the form y=fxgx…

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: Given: Function f(x) = 3x - cosx  To Find The x - values for which the given function is not…

Q: 19. Determine the following function if continuous at 2 f(x) = (,) ;at x = -1 + 1 A. discontinuous…

A: Explanation of the answer is as follows

Q: a. On what interval(s) is f(x) increasing? Justify. b. What is the concavity of f(x) at x=2?…

A: Part(a). From the given graph f(x) is increasing on the interval (-4,1) , Because f'(x)&gt;0   (…

Q: Describe the interval(s) on which the function is continuous.

A: Given: Describe the interval(s) on which the function is continuous. f(x)=sec πx4Clearly from the…

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A:

Q: Based on your work in part a, on what interval(s) is f(x) continuous?

A:

Q: find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

A: Consider two functions f(x),g(x) defined for all real numbers. Let the two functions be continuous…

Q: Is the following function continuous F(x)=x cot 5x

A:

Q: Let f(x) = 17 – x? The slope of the tangent line to the graph of f(x) at the point ( – 4, 1) is The…

A:

Q: Find the absolute extrema of the function on the closed interval.                          y = tan…

A: Given function is y=tanx8.

Q: Find the intervals on which f is increasing and decreasing. f(y) = sin y - y cos y on 2' 2

A: Find your answer below

Q: At what points are the functions continuous? x tan x y = x² + 1

A: Given function is y=xtanxx2+1.

Q: Is the function continuous  f(x) = e^x / 1 - e^x

A: We need to check the continuity of the function

Q: 10. Consider the function defined by f(x) = Vr. Is ƒ differentiable at r = 1? at r = 0? at %D x =…

A:

Q: On the graph of f(x) = tanx and the interval [ − π, π ), for what value(s) of x does f(x) = 1?

A:

Q: a) For which values of a and b in R is f(x) continuous on (-infinity, pi/2)? b) For which values of…

A: Given function is f(x)=x+a, x≤0bcos(x)+asin(x) , 0&lt;x≤π4btan(x), x≥π4 If f(x) is continuous on…

Q: 16.C. If f is defined and continuous on R? to R and if f(xo) > 0, then is f positive on some…

A: Consider the provided question,   We need to show that, f is strictly positive on some neighborhood…

Q: Assume that f(x) is everywhere continuous and it is given to you that f(x)+ 10 lim a - 5 -10 It…

A: The formula to find the slope of the tangent line to the curve y = f(x) at point x = a is,…

Q: Find number k, so that f is continuous at every point. tan kx f(x) = x 4x+3 k2, x 20 O O and= Cannot…

A: The function is given by fx = tankxx ,x&lt;04x+3k2 ,x≥0 To evaluate : The value of k so that f is…

Q: Given (x², if 0sxsb f(x) = if b<x %3D (a) Determine a value of b so that f is continuous at b. (b)…

A:

Q: Consider f(x) = #3/5. Is f(x) differentiable at x=0? Is f(x) continuous at x=0?

A: The given function is,

Q: 17.Determine the following function if continuous at p(x) = 3x? – x +5 ;at x = 1 A. discontinuous at…

A:

Q: Assume that f(x) is everywhere continuous and it is given to you that f(x) + 7 lim %3D х — 6 х—6 It…

A:

Q: Is the following piecewise defined function f(x) continuous at x = = 0, [cos(x), x≤0 f(x) = x²+x+1,…

A: The given function is: fx=cos x,       x≤0x2+x+1,  x&gt;0 Check whether the function is continuous…

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

A: Consider: f(x)=tanx4, −1&lt;x&lt;1x,              x≥1x,              x≤−1  tanx4is continuous on…

Q: x = 0 f(x) sin z x +0 а) х — 0. ? b) х — 4т. ?

A:

Q: Describe the interval(s) on which the function is continuous. f(x) = cos 1/x

A: Given- fx=cos1x To find- The intervals on which the function is continuous. Concept Used- As we know…

Q: What is the largest interval containing zero on which f (x) = sin x is one-to-one?

A: A function f: X -&gt; Y is said to be one-to-one, if the images of distinct elements of X under f…

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: given that  f(x)=tanx2

Q: The graph of the derivativef'of a function f over the interval (a, b) is shown. y =f(x) (a) On what…

A: If f'x is positive then fx is increasing If  f'x is negative then fx is decreasing

Q: Where is f(x) = e* continuous?

A:

Q: Assume that f(x) is everywhere continuous and it is given to you that f(x) + 8 lim x→2 x - 2 = -4 It…

A: Consider the given expression limx→2fx+8x-2=-4 Or, -4=limx→2fx+8x-2                            …1…

Q: Consider the following function and answer the following questions. sin x f(x) = [-5,5] by [-5,5],…

A:

Q: The derivative of a function f is given by f'(x) = esin for 0 < x < 9. On what intervals is f…

A:

Q: * Suppose -x if x π - (a) Find f'(x) (b) Find f"(T) or show that f is not twice differentiable at 7

A: Given Function  f(x) = -x    if x&lt;0sinx  if 0≤x≤ππ-x  if x≥π   a) i) we have to find f'(x) at x=0…

Q: If f (x)  =In  (2x + x Sin x), use the graphs of  f ,f' , and f"to estimate the intervals of…

A: Given: f(x) = ln(2x+xsin…

Q: · For what values of x such that 0 < Is 27, does the graph of f(x) = x - tan r have a rizontal…

A: We will solve the following

Q: Let f(x) = The slope of the tangent line to the graph of f(x) at 33 - the point (8, 5) is The…

A: To find the slope and equation of the tangent line of f(x) at the point (8,5).

Q: Decide if the function below is continuous or not using the three conditions of continuity. { x*sin…

A:

Q: Graph the function and observe where it is discontinuous. f(x, y) = e1/(x - y) fis discontinuous at…

A:

Q: If f(x) is continuous at x = c, then so is If (x)|.

A: To determine: The given statement is true or false. Given statement: If f(x) is continuous at x=c,…

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…

Q: For f(x)=sin⁡x/2cos⁡x−1, at what values in the interval [−π,π] is f discontinuous?

A:

Q: For what value of a is the function continuous at every x?

A:

Q: For what value or values of the constant m, if any, is ( sin 2x, f(x) = Imx, x 0 тх, a. continuous…

A:

Q: Suppose that y = f(x) is a continuous function defined on the interval from z = 0 to z = E. Below is…

A: