What conditions must be satisfied by a function if it is to be con-tinuous at an interior point of its domain? At an endpoint?

Q: Given the graph of f', the derivative of f, locate all extrema of f. JUSTIFY. Minimum at x = because…

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Q: Find all points where the function is discontinuous.

A: Function is discontinuous at points where graph breaks. So, we have to find point where the given…

Q: Will a function that is differentiable on a given interval always be continuous on that interval?…

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Q: What are the basic properties of limits of functions of two independent variables?

A: What are the basic properties of limits of functions of two independent variables?

Q: Verify Rolle's theorem for the function f(x) = 2x2 – 20x + 33 on the interval [2, 8]. -

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Q: Consider the function defined on the indicated interval. f(x) = 2x – 30x + 144x – 220, [5, 8] %3D…

A: To find maximum and minimum of the given function in interval [5, 8] fx=2x3−30x2+144x−220

Q: Is there a function that is both even and odd?

A: Yes, f(x)=0 is both even and odd.

Q: The graph of f is given above. Which statement regarding the local (or relative) minimum of f is…

A: Relative minima is the point where slope of the graph is zero and there is a change from negative…

Q: Is the secant function even, odd, or neither? Is its graphsymmetric? With respect to what?

A: The given function is secant function y=secx

Q: How is a function’s differentiability at a point related to its continuity there, if at all?

A: If a function is differentiable at any point there it has to be continuous. For example: y= x^2 has…

Q: Is it possible for a function to satisfy f(x) > 0, f′(x) > 0, andf ″(x) < 0 on an interval?…

A: We want function that is: 1. positive on interval I since fx>0   2. increasing on interval I…

Q: Find the points of discontinuity of the function f(x)=arctan1x if they exist.

A: The given function is not defined at x = 0. Now the left hand limit at x = 0 is, And the right hand…

Q: Please illustrate the difference between a function being continuous and differentiable by…

A: We have to  illustrate the difference between a function being continuous and differentiable…

Q: Will a function that is differentiable on a given interval always be continuous on that interval?…

A: Given the statement that " Will a function that is differentiable on a given interval always be…

Q: Find an example of a function on the real line, R, that is contin- uous everywhere except at x = on…

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Q: sketch to graph the function f(x) = In(x + 2) – 1. %3D

A: f(x)=ln(x+2)-1Now, putting value of x=-1f(-1) =ln(-1+2)-1           [ln1=0]           =0-1…

Q: Determine if the function f(x)=arctanx is convex downward or upward at the point x=1?

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Q: What does it mean for a function to be right-continuous at a point?

A: A function f is right continuous at a point c if it is defined on an interval [c, d] lying to the…

Q: A fixed point of a function f is a number c in its domain that satisfies f(c).  In other words, the…

A: Given: A fixed point of a function f is a number c in its domain that satisfies f(c).

Q: Show that f (x) = x3 - 3x is an odd function. Explain why its graph is symmetric about the origin.

A: Given, fx=x3-3x

Q: find and sketch the domain of the function f(x,y)= Suqare root 2x-y

A: f(x,y)=2x-yAs we know that domain refer to set of positive values  while range is the set of…

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: Sketch one possible graph of a function f(x) defined on R that satisfies all the listed conditions.…

A: Plotting Graph.

Q: If f(z) is analytic function show that:

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Q: Let f(x) be an EVEN function. If the point (2, 3) belongs to f, then another point likely to belong…

A: Let f(x) be an EVEN function.

Q: 3) If a function is continuaus at x=a, then it is differentiaoe at x-a, yes? or NO? why ?

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Q: The function f  whose graph is given has a discontinuity at x=4 since  does not exist. Prove true…

A: Topic:- function

Q: explain why the function has at least one zero in the given interval. f(x) = x^3+ 5x-3 intervals…

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Q: An even function is symmetric with respect to the________

A: An even function is symmetric with respect to the________

Q: (+) Sketch the midline and the graph of the function f(x) = - 3 - 4 sin 8+ 7- 5. 4 2 -4 -3 -2 -1 -1…

A: See the graph below

Q: Suppose that f is a function defined as f(x) = 5x3 + 3x2 + x + 3. Find an equation for the tangent…

A: f(x)=5x3+3x2+x+3Derivative formuladdxxn=n xn-1

Q: find a point c satisfying the conclusion of the MVT for the given function and interval.

A: Given ,y = Cos x - Sin x      0,2πf(x) = Cos x - Sin x

Q: Explain why functions with cusps are not differentiable even though they are continuous.

A: Derivative is a slope, defined by a limit.   In order for a derivative to exist, it needs to be…

Q: Give the three conditions that must be satisfied by a function to be continuous at a point.

A: We have to write  the three conditions that must be satisfied by a function to be continuous at a…

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

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Q: Determine from the graph whether the function has any absolute extreme values on [a, b]. Then…

A: For given graph, Absolute Maximum is at x = d. and  Absolute minimum does not exist.

Q: List the points in the graph in the interval 1 <x<7 at which the function is not differentiable 18-

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Q: Explain Why functions with cusps are not differentiable even though they are continuous.

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Q: Is the function continuous or discontinuous? If discontinuous, what condition is not satisfied?

A: Given:

Q: Determine the set of points at which the function is continuous

A: f (x, y, z) = sin-1 (x2 + y2 + z2) = t (Let's say)Hence, sin t = (x2 + y2 + z2)

Q: Suppose f is a function with domain [a,b]. If f is an odd function, what can be deduced about a and…

A: According to question f is a function with domain [a, b]  And f is an odd function.

Q: If f is even and differentiable function, the x = 0 is a critcal number of f. True or False

A: Known fact: For even differentiable function, 0 is a critical number.

Q: Sketch a graph of the function f(x) : 2 sin +1 6+ 4 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 -9 -8 4 5 -2 -3 -4…

A: Given: The function

Q: Describe the intervals on which the function is continuous.                           f(x) = (4x2 +…

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Q: Find a function f that satisfies the conditions. "(a) --Na (1) - 5, (4) - -1

A: Given Data: The second derivative of the function is: f"x=x-3/2 ......1 The value of the first…

Q: Can you conclude anything about the extreme values of a continu-ous function on an open interval? On…

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Q: What conditions have to be checked to determine if a function is "well defined"?  How would I show…

A: Let the function beThen we need to check 3 conditions to prove that the function is Well definedThey…