How would you "remove the discontinuity" of f? In other words, how would you define f(2) in order to make f continuous at 2? f(x) x^2-x-2/x-2

Q: Use interval notation to indicate where f(x)=x-7/(x-5)(x+5) is continuous.   "f" is continuous on…

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Q: f(x) = 9x² - 4 at x = 1

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Q: 2. When can we say that a function is continuous at an interval?

A: We know that when a function does not have any discontinuity, then it is a continuous function. It…

Q: Use interval notation to indicate where x2 – 1 - f(x) = x2 – 7x + 6 - is continuous. f is continuous…

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Q: Use the limit definition of the derivative to compute f'(x) for f(x)= 1/ sqrt of x

A: Given, f(x)=1x

Q: Find the slope of the tangent line to the graph of f(x) = x³ + x at x = 3 using the limits…

A: Given- fx=x3+x To find- The slope of the tangent line to the above function at x = 3 using the…

Q: When is a function continuous over a closed interval?

A: A function is continuous over a closed interval when it is defined at all points in the interval…

Q: What can be said about the extreme values of a function that is continuous on a closed interval?

A: To Determine: What can be said about the extreme values of a function that iscontinuous on a closed…

Q: Use derivative rules to compute f'(-1) given f (x) = -4x8-32x - 4.

A: f(x)=-4x8-32x-4Formula: xn'=n xn-1

Q: is the function continuous at x=5 if f(x)={x2-4x-5/x-5,     x5

A: Given: f(x)=x2-4x-5x-5  ,   x<5x+1            ,  x≥5

Q: use interval notation to indicate  where f(x)=x-7 divided by (x-2)(x+1) continuous  f is…

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Q: If f is continuous on (-x, ∞), what can you say about its graph?

A: If f is continuous on (-oo oo) what can you say about its graph?

Q: Use secant method to estimate a root for function f(x)= x3 + 2.7x+ 2.6 = 0, starting for interval…

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Q: where is the function f(x)= llxll-2 continuous (or discontinuous)?

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Q: a) f'(-3) where f(x) = 5-3x

A: Derivative using definition

Q: Find f'(x) from f(x)= = 2x³x²x+ 2 using the definition of a derivative. (Do not include "f'(x) =" in…

A: Use simple differentiation formula.

Q: What is the relationship between functions whose limits can be obtained by direct substitution and…

A: We need to define the relation between a limit and continuous function.

Q: How would you "remove the discontinuity" of f? In other words, how would you define f(2) in order to…

A: Given : fx = x2-x-2x-2

Q: Determine whether the function is continuous at the given points. x+2 if x22 : 2,0 x if x<2 f(x) =…

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Q: How would you "remove the discontinuity" of f? In other words, how would you define f(3) in order to…

A: The given function is: f(x)=x2-x-6x-3

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: Find the slope.

Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

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Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?

A: Suppose   are continuous function at then rational function is continuous at   if .

Q: Suppose we know that f(x) is continuous and differentiable on the interval [-7,0], that f(-7) = -3…

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Q: Suppose f is a f(8(x))=2x² and differentiable function where 2x f'(x)=2+ f (x). Show that g'(x)=…

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Q: For the function f, how would you remove the discontinuity? In other words, how would you define…

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Q: Give an example of a function that is defined for all real numbers, is continuous everywhere, but…

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Q: Determine the open interval(s) in which f(x) = 2x3 – 6x² is increasing or decreasing. Also, ocate…

A: Given        fx=2x3-6x2

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: 3 Show that f(x)= 1x-5 is NOT differentiable at 5 by using the defini tion of the derivative, (Start…

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Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

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Q: 3. Use the limit definition of a derivative to find f'(x) if f(x) = 3x2 - 5x %3D

A: f(x)=3x2-5x

Q: I'm confused on how to put a piecewise function into interval notation

A: To rewrite the definition of the given function using interval notation

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

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Q: Consider the following function and closed interval. f(x) = x3 - 4x2 – 16x + 5, [-4, 4] Is f…

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

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Q: For what value of the constant c is the function f continuous on (-∞, 00) ? if x < 3 cx2 + 8x F(x) =…

A: To find: The value of c if function is continuous at -∞,∞. Given: The function is fx=cx2+8x   if…

Q: Find the value of K that makes 4-x2 f(x) = {2-x if x # 2 2K if x = 2 continuous at x = 2 ?

A: Find the value of k

Q: Apply the first derivative test to indentify all relative extrema. f(x) = ¹²-2x+1

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Q: Show that f (x) = 1x-5| is NOT differentiable at 5 by using the definition of the derivative, (Start…

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Q: Explain why f(x)=3x^2+1 is continuous at x=-2

A: Consider the function  f(x)=3x2+1

Q: 3lim %3D f(x+h)-f(x) to find f'(x) for f(x) = -4x2+2x+3. = (),f

A: NOTE: Refresh your page if you can't see any equations. . substitute x+h for x

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: Is the function continuous at the point being approached?

A: The given function is limy→1sec(y*sec2y-tan2y-1)   We have to check whether this function is…

Q: Can the Mean Value Theorem be applied to the function f(x) = 1/x2 on the interval [−2, 1]? Explain

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Q: How would you "remove the discontinuity" of f? In other words, how would you define f(3) in order to…

A: Given, fx = x2-2x-3x-3  We have to define f3 in order to make f is continuous at 3.

Q: Determine at which points, the function 97× ナ x²if x E RIQ f(x)= is continuous.

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Q: Suppose fx) is continuous on the interval [0,10] and that f(x) = 0 only when x = 4. If f(5)< 0, what…

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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.