true or false? if a function is differntiable at an input then it must be continuous at the input

Q: True or False suppose a function f(x) is differentiable everywhere. Further suppose f : ℝ -> ℝ.…

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Q: If a function has a finite derivative at a given point , prove that it is continuous at that point .…

A: Let any function f(x) has a finite derivative at any given point say (c) It means…

Q: Determine the intervals where the function f(x)= lnx/x is increasing and where it is decreasing.

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Q: Explain how to find the extrema of a continuous function on a closed interval [a, b].

A: First, you have to find f'(x) Then solve f ' (x)=0 to find the critical points.  Take the critical…

Q: Use Linear Approximation to estimate Af = f (3.01) – f(3) for f(x) = x*. (Use decimal notation. Give…

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Q: Describe the properties of continuous  function?

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Q: Give a graphical example of a function, f(x), with the given characteristics: ˆ f(x) is not…

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Q: List the  Properties of Continuous Functions?

A: given,       List the  Properties of Continuous Functions

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

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Q: True False Suppose f(x) is continuous everywhere. Must f(x) attain an absolute maximum somewhere on…

A: Extreme value theorem states that if f(x) is continuous on closed interval I, then f(x) attains…

Q: What does it mean for a function to be continuous on an interval? Give examples to illustrate the…

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Q: ax²-3 -,х> 1 x-1 Value of a and b that will make f (x) = continuous everywhere are ... lbx + 2, х <…

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Q: Definition: "The second derivative of a function f with respect to the variable x evaluated at x = a…

A: Since the second derivative of a function f is the derivative of the derivative of function f.

Q: How do you find the length of the graph of a smooth function over a closed interval? Give an…

A: known fact:

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

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Q: continuous at x- 3? Why or why not? Is the function given by f(x) = ! 3*+5, for x 3,

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Q: What does it mean for a function to be continuous on an interval? Give examples to illustrate the…

A: In simple terms, if the graph of a function can be drawn without lifting the pen from the paper, we…

Q: True or False, an even function is never invertible.  I'm having trouble understanding this

A: From the given information it is needed to prove whether even function is invertible or not.A…

Q: When can we say that a function is continuous at a number?

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: Find the relative extrema of the function g(x) = x sech x. Use a graphing utility to confirm your…

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Q: 1) If possible, give an example of where a function is differentiable at a point but not continuous…

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Q: The vertical line test to determine whethera curve is the graph of a function states: If every…

A: We have to prove that a vertical line in the xy plane intersects a given curve in at most one point…

Q: 8. If a continuous, differentiable function f is equal to 2 at x = 3 and at x = 5, what can you say…

A: Given that if a continuous, differentiable function f is equal to 2 atx=3 and at x=5, Our Aim is to…

Q: If a function is differentiable at a point then it is continuous at that point. False True

A: The given statement is true . i.e. if a function is differentiable at a point then it is continuous…

Q: Domain of function f(x) = ln is (0, 2) O True False

A: Since you are asking multiple questions. We are answering only the first question. We have to check…

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: The given statement is false.Because it is not necessary that if a function is continuous then it…

Q: Show that the function f(x)=x|x| is continuous and differentiable at x = 0

A: To show that f(x)=xx is continuous at x=0 To show that limx→0xx=00=0 use piecewise definition for…

Q: true or false?  Continuous functions have a tangent line at all points.

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Q: 1) If possible, give an example of where a function is differentiable at a point but not continuous…

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Q: Find the open interval(s) where the function is increasing and decreasing. f(x) = - x + 3 Show work…

A: For a function f(x): f(x) is increasing in the interval where f'(x) &gt;0 f(x) is decreasing in the…

Q: A wire of length x is bent into the shape of a circle.(a) Express the circumference C of the circle…

A: Given: A wire of length x is bent into the shape of a circle.

Q: ) A wire of length x is bent into the shape of a circle. Express the area A of the circle as a…

A: Length of wire =xgiven   So, circumference of given circle=x    Let radius of circle be  r…

Q: Define the term Intermediate Value Theorem for Continuous Functions?

A: Intermediate value theorem states that, If “f” be a continuous function over a closed interval [a,…

Q: A fixed point of a function f is a value x where f(x) = x.Show that if f is differentiable on an…

A: Suppose fx be any function, then a fixed point of the function f(x) is a value of x  when fx=x Now,…

Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

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Q: True or false The slope of th tangent line to a dfferentiable function f at the point (2,f(x)) is

A: The slope of the tangent line to a differentiable function f at the point (2, f(x)) is

Q: A wire of length x is bent into the shape of a square.(a) Express the perimeter p of the square as a…

A: Consider the given length of wire x into the shape of a square

Q: What does it mean for a function to be continuous on an interval?Give examples to illustrate the…

A: For open intervalIf f:(a, b)→ℝ is defined on an open interval, then f is continuous on (a, b) if and…

Q: Is it true that a continuous function that is never zero on an interval never changes sign on that…

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Q: True False Suppose f(x) is differentiable at x=a. Then f also continuous at x=a.

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Q: Determine where the function f(x) is continuous. f(x) = Vx-1 The function is continuous on the…

A: If f(x) is defined then it is continuous

Q: What are the intervals where the function has a positive first derivative? (d,e) (b,c) (c,d) (e,f)…

A: Recall the fact that the first derivative is positive if the function is increasing in that…

Q: Redefine function f at x = 2 so that it is continuous everywhere. 2x + 1 f(x) x + 2 x = 2 | %3D

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

A: A function fx is said to be continuous at a point at x=c if 1. fc is defined and exists 2.…

Q: Use Linear Approximation to estimate Af = f (2.01) – f(2) for f(x) = x“. (Use decimal notation. Give…

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Q: 4. Question Verify Mean Value Theorem for the function f(x) = X in interval [0,9] %3D

A: Verification of MVT  As per our guidelines we are supposed to answer only first question Kindly…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.