57. Find a formula for a function ƒ that satisfies the following conditions: lim f(x) = 0, lim f(x) = -o, f(2) = 0, lim f(x) = ∞, lim f(x) = -00 x→3-

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A: Given the piecewise function :

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Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

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A: Given: The function satisfies the condition…

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Q: Prove the limit statements

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Q: 2x+1 if x 2 Determine the one-sided limit lim f(x). x-2- 2

A: The given function is:

Q: 1) The graph of a function y = f(x) has the line y = -2x + 5 as its tangent at the point (3, 10).…

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Q: (a) If f(x) = 3x3 – 2x, find a formula for f'(x). (b) Illustrate this formula by comparing the…

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Q: 2x + 1 If t(x) find lim,-o t(x) %3D 8x + 1

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Q: Q.4: Prove or disprove, lim f(x) = 4 If f(x) = x # 2 x = 2' I-2

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Q: Suppose a function f satisfies f(3+h) – 2 lim = 7. Find an equation for the line tangent to the…

A: Let

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Q: 1. Consider the function f(x, y) = 2y (a) Show that lim (x,y)(0,0) f(x, y) does not exist by using…

A: Note: if a limit exists at a point,it must be the same limit along any path approaching that point.…

Q: 2. Consider the function: + 3 if x 2 %3D 17 if x = 2. %3D Find lim, 2 f(x).

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Q: Verify numerically that:

A: To verify: limh→0eh-1h=1

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A: cost function C(x)=15,000+45 x

Q: When the function f(x) satisfies f(1) =1,f'(1)= 3 obtain a value of lim/ (2)" -1 x→1 x² – 1

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Q: 4. Evaluate the limits of the following functions: a) limsinx x-0 sin x-tan x 6 b) lim x-2 x2+2x-8)…

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Q: * + 2, if x 0' (a) Find lim f(x). (b) Give a simple reason why f is discontinuous at 0.

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Q: x' + 2, if x 0 (a) Find lim f(x).

A: Since , the only point of discontinuity can be zero . For rest of the points on ℝ the function is…

Q: The function values for h(x) near x = 1 are given in the table below. -0.10–0.05–0.011 2.01 2.05…

A: Given

Q: ( Describe the end behavior of the function h(x) shown, using limits at infinity. 3 2.5 2 1.5 1 0.5…

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Q: If lim as t approaches 4 of the function ((g(x)-6)/(t-1))=1. Find lim t approaches 4 of g(t).

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Q: (6) Draw the graph of a (a) function ƒ satisfying Y S(1) = 2, S is continuous at 1. What is lim,→1…

A: f(1)=2f is continuous at 1

Q: x4/7 – 1 lim f'(a) where x→-1 x + 1 f(x) = and a = x4/7 lim x + 1 1 х>-1 II

A: Explanation of the solution is given below...

Q: 11. If we are told that the tangent line to the graph of y = f(x) at the point x = 3 is y = -2x + 1…

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Q: 10- In parts (A)-(C), find the indicated quantity for y = f(x) = 5- x. f( - 1)- f(- 2) (A) (-1)-(-2)…

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Q: 2. The derivative of a functionfwith respect to x is given by (w)-r(x) a) f'(x) = limwx e) f"(x) =…

A: The derivative of a function f with respect to x is given by

Q: 1 | 1. lim f(x), where f (x) = x→1 x² – 1° f (x) f (x) 1.002 0.998 1.001 0.999 1.0005 0.9995 1.00001…

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Q: Show that the function is continuous at the given value. f(x) = 3x, c = 2 The function f(x) is…

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Q: For f(x) = 2x³ - 2, find ƒ '(x) using the definition f '(x) = lim f(x+h)-f(x) h h→0 f'(x) = Using…

A: Let's find.

Q: True and False. (1) _A function f is continuous at x = a if and only if limf(x) = f(a). y=x² -10x+5…

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Q: 1. Show that for all f e L'(R) lim da = 0.

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Q: (2+h)* Use the definition of the derivative to evaluate lim h+0 h

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Q: f(0) = 1, f"(x) < 0 for x # 0, lim f'(x) = +0, lim f'(x) = -00

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Q: - Consider the function f(r) = xe on the interval [0, 00) f'(x) f(x) (a) Compute f'(x) and find the…

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Q: ,if x> -3 Given the function f(x) =' 3 ,ifx S-3 is continuous at x=-3

A: A function                      fx=x2-9x+3,   if x&lt;-33,             if x≤-3 We have to answer the…

Q: b. For what value of (k) is the function y=f(x) continuous at x-3. x3-3x2-4x+12 x + 3 x-3 f(x) = %3D…

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