8) Assume that 2 + Va if x >1 if x < 1 f(x) = Determine whether or not f is continuous at x = state your conclusion. 1. Justify your answer and

Q: is continuous at x=3, f (-1) =6 ? + a, x # 3 3b, x 3 ontinuous at x=2? - x > 0

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

A: Given f(x) is continuous and differentiable and f(3) = f(s) = 2Concept Roll's Theorem If f(x) is…

Q: (-х+а, х < —1 If f(x) = {x² + 5, –1 < x < 2 is continuous then х — b, х 2 2 a + b =?

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Q: Q7 Show that f is continuous on (-∞, 0) sinxif x - 4

A: Trigonometric function with sine and cosine in continuous in its domain.    Here in this question,…

Q: Either a function is not differentiable at a point or it is continuous at that point. O True False

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Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

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Q: п-(х-4)" 22и. (2n — 1) Ax) =En=0 n:

A: Solution of given problem as follow

Q: verify mean value theorem for the function f(x)=4x3 over ihe interval [0,2 ]?

A: verify mean value theorem for the function f(x)=4x3 over ihe interval [0,2 ]

Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: Find the equation of the tangent line of f(x) = sqrt(x+1) at x = 0 using the definition of limits.

A: To find: The equation of tangent of line. Given: The function is f(x)=x+1. Concept used: Slope…

Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

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Q: 4. Is the function f integrable over the interval [-4,1]? Briefly justify your answer. 2x2 + 5x – 3…

A: Solution  Question 4  Given,  fx = 2x2+5x-3x+3  We have to find the function is integrable in the…

Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x&lt;4-x+7,   for  x&gt;4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

Q: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a, b],…

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Q: Give an example of a function that is continuous on -∞ < x < o but is not differentiable at x = 3.

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Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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

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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?

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A: Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal…

Q: H(x) = L, [At) +A-1) ]dt

A: Question derivative of function.

Q: State both the converse and the contrapositive of the assertion “Every differentiable function is…

A: We will make use of fundamental definition of these terms.

Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

A:

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Q: 10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not…

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Q: Suppose that fis a continuous function and that1. f(x)dx=-1 and L(x)dx = 5, find the value of…

A: suppose that f is continuous function . We have to find the following

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: Could the limit as xà1 of f(x)=(x+sinx)/(1+x+cosx) be found simply by substituting 1 into the…

A: Given function f(x)=(x+ sin (x))/(1+x+ cos (x)) Now we will evaluate limit of f(X) as X tends to 1…

Q: 9. Is the function defined by gon3 – 3 if 2. continuous at r= 2? differentiable at x = 2?

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Q: Given the piecewise function f(x) = Why is f not differentiable at x = 5? Of is continuous at x = :5…

A: This question is based on continuity of function.

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: Suppose for sume function f we heve its derivative, f'cx) = e*sin(x), on the %3D interval o< x< ar.…

A: fx is a function such that f'x=exsinx on the interval 0&lt;x&lt;2π We have to determine where the…

Q: Express the limit as a definite integral on the given interval.

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Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: 7. Where is f(x.y)= continuous? Do not just write an answer, show your work or give any necessary…

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Q: In(8z) Siven f(z) the derivative f'(x) is 8. %3D O 8 8x o 1 O 78z 1 8x 1/8

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Q: Use Taylor’s inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when 0.5 ≤ x ≤…

A: We have to use Taylor’s inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when…

Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

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Q: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

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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: let  f(x)=  x+2  if x1 Find the value of k that will make f continuous on (-∞,∞)

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Q: Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x…

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Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: Does f(x) 1-V1-x² continuous on the interval [-1, 1]?

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Q: Is f continuous at x = 1?

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Q: (i) Consider the function such that f(x) = 2x if 0SxS1 and f(x) = x-1 if x> 1. Is f continuous over…

A:

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.