3. Using one sided limits, determine whether or not the function f(x) below is continuous at x = 3. x2 – 1, for x< 3 2x – 4, for r > 3 f(x) =

Q: Q2. Let f: R → R be a function such that f(x) = x sin f is defined at xo, where the value of 8…

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Q: Is the limit of f (x) as x approaches c always equal to f (c)? Why or why not?

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Q: + [ƒ(2)₁ Suppose that fand gare continuous functions such that 1 [ g(x)dz -3, find f(x)dx= 2 and +…

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Q: Consider g(x) = x!/5. Is g(x) differentiable at x=0? Is g(x) continuous at x=0?

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Q: Let f(x) { Calculate the following limits. Enter "DNE" if the limit do f(x) = 10- x - x² if x ≤ 4 if…

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Q: (5) Use the limit definition of derivative to prove the following: (a) For any a e R, (f(ax))' =…

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Q: Let f(x) = { *, if x= 2 ; for the eax if x + 2 function to be continuous at x = 2 the value of a is

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Q: Suppose f' (x) = g (x) (x + 1) (x – 2)´, where g (s) is a continuous function which is always…

A: When f'(x)&gt;0 then function increasing when f'(x)&lt;0 then function decreasing

Q: 9. If f is continuous and 1| f(x)dx = 8, show that f takes on the value 4 at least once on the…

A: We need to show f takes value 4.

Q: 8. Suppose that f is a continuous function such that f'(x) > 0 for all æ, f(0) = 0, and f(1) = 1. If…

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Q: If functions ƒ(x) and g(x) are continuous for

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Q: . Which statement is TRUE about the limit of the function f as x approaches 1? sx – 1 if x > 1 (-x²…

A: A. The limit of f as x approaches 1 is 0 False explanation :- The limit of f as x approaches 1 is…

Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

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Q: Show that the absolute-value function y = t(x) = |x − 5| is NOT differentiable at x = 5. (Hint: by…

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Q: 2e What is the limit of the function f (x) = as x + xo ? 1-e

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Q: 35. Given that f(z) is a continuous even function, then A 0 B D

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Q: Suppose f : R → R is a continuous function with the property that f(x) = 0 for every x E Q. Prove…

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Q: Use limits to determine if f(x) = 1 is continuous at x = 0. (z+2)?

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Q: given f(x) = (2x+1)/(x+3), use the limit definition to find the tangent line to graph of f(x) at x=0

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Q: 2- For what value of the costant c is the function continuous at every number? F(x) = {x+c if x<2…

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Q: Show that the limit of the function f(x,y) = at (0,0) does not exist. (x+y)² x² + y²

A: Limit of a Function: Like a single-variable function, a multi-variable function can also have limit.…

Q: Let f(x) = /20 – x. Compute f'(4) using the limit definition f'(4) - - Find an equation of the…

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

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Q: If f(2) is a continuous function at a point z, , then f(z) is differentiable at z, . But the…

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Q: 10.C. If f is defined and continuous on R to R and if f(xo) > 0, then is f positive on some…

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Q: that makes y continuous but not differentiable by writing the required procedures to that If: X≥0…

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Q: 7. Find the limit as x approaches 0. F V I 2 2 O infinity O limit does not exist Oo .

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Q: 1 (a) What type of discontinuity does the function g(x)=- have at el/x – 1 x=0 ? Explain. (b) For…

A: This question is from limits and continuity.

Q: dy -) using definition with limit of the following: dr 4. Find the differentiation (- y = /2x + 1.

A: We need to find the differentiation of y=2x+1 using the definition of limit. Now, according to the…

Q: 5. If f (2) = 5 for the continuous function f (x), calculate the following limit value | F(t) dt lim…

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Q: Use limits to determine if f(x) = is continuous at x = 1. z-2

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Q: True or false 1. If the left- and right-hand limits of f(x) as x→ c exists and are equal,Then f(x)…

A: If f(x) be a function on a subset of real number and c be point in domain of f then f is continuous…

Q: 10 If f is a continuous function and F(x)=f(x) for all x€R, then | f(Gx)dx=?

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Q: Q3) If the function (2x + 1 +2 x > h) XSh f(x) having limit at x = h. Find the value of h. Q4) f(x,…

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Q: Let f (x) = In(x + 2). Use the definition of the derivative and your now expanded knowledge of…

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Q: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

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Q: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) 9. 13 2 3 What…

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Q: 2 If f is continuous on [0, 2] and f(x) dx = 5, find the value of | f(æ – 2) dæ.

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Q: . Is the function continuous on the interval (4, 10)? (x + 1 if x > 8 f(x) = E) + 7 if x < 8 A.…

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Q: S 10 – x – a? if x 1 Calculate the following limits. Enter "DNE" if the limit does not exist. 2x +…

A: The given function is f(x)=10-x-x2if x≤12x+6if x&gt;1 We have to calculate,  a) limx→1-f(x)=?b)…

Q: If f is a continuous function and F'(x)=f(x) for all x € R, then - x)dx=?

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Q: 4. Use the limit definition of the derivative to test whether the following function f(x), given by…

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Q: . Is f(x)= Vx + 1 continuous at x == -1? Yes, because all functions are continuous No, because the…

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Q: 5. Consider the function S 2r – 1, si x < 2 f(x) = 6-x, si x 2 2. The Limit x 2 f(x) is:

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Q: Express the limit as a definite integral. [Hint: Consider f(x) = x*.] n lim n5 i = 1 1 7n 2n dx

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Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

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Q: Let f(x)=√18 x. Compute f'(2) using the limit definition f'(2) = Find an equation of the tangent…

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Q: Suppose that f (x) is a continuous function. 3 If | f(x) dx=5, then what is the value of z - f(x)]…

A: Given, ∫13f(x) dx =5Now,∫13[x -f(x)] dx= ∫13x dx -∫13f(x) dx =x2213 -5…

Q: Suppose that f(x) is a continuous function on the interval [0, T] . If f(x)=(sin x)ª for 0<x<T, then…

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Q: x+4 Which will prove that f(x) is continuous at C= -4? x2+16 1. f(-4)=0 II. lim f(x)=0 III. f(x)=…

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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.