4. Sketch the graph of an example of a function f that satisfies all of the given conditions lim f(x) = –1 T→3- lim f(x) = 2 f(3) = 1 x→3+

Q: Determine whether the function x2 + 2 x > 2 f(x) = x = 2 is continuous at the 4х — 2 x < 2 given…

A: First of all we will find the left hand limit at X equal to 2 and then find the right hand limit X…

Q: 21. If f(x) = In x, then lim f (x) – f(3) is x→3 x – 3 1 (A) (B) e (C) In 3 (D) nonexistent

A: topic - limits

Q: 2.15 Suppose there exists a E R such that x > a implies f(x) > 0. Prove: 1 lim f(x) = 0 + lim 0. %3D…

A: We have to prove the given limit.

Q: 2. Use the ɛ-d definition of the limit of a function to prove that lim = 3. I-»3 T – 2

A: Let  I  be an open interval containing  c , and let  f  be a function defined on  I , except…

Q: (4) Let f(x) be the function whose domain is all of R given by the rule 42 if r € Z and f(x) = 10…

A:

Q: Plot the graphs of u(x) = 1+ |x – and I(x) = sin x on the same set of axes. What can you say about…

A: Sandwich theorem of limit states that if our original function is sandwiched between two functions…

Q: 1. Prove the following limit. a) f(x)=x²+2x+6 where lim f (x)= 21 b) lim x-x+1=-5 x3 c) limx =8 x→2

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Q: Let f(x) = 4x² + 6x + 2. According to the definition, f'(x) lim h→0 (Enter the limit in reduced…

A: Given f(x)=4x2+6x+2

Q: If f(x) is differentiable at X =c then lim f(x) must exist and f(c) must be defined

A:

Q: 1. Evaluate the limit for the graph lim f (x). x→1" f(x) 51 4- 3 2 1- -3 -2 -1 1 2 3 4 -1 а. 1 c.…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: For the function f(x) (X^2-3 if -3 ≤x2 C) is f continuous at x=2? D) does lim f(x) exist at x->4^-?…

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Q: Let f(x) = 2x² + 2x + 3. According to the definition, f'(x) = lim h→0 (Enter the limit in reduced…

A: the soluton is following.

Q: 3. is a type of discontinuity when the lim and lim f(x) = M where L# M and either f(a) does not…

A: Discontinuity 1: When the limx -&gt; a- f(x) = L and limx -&gt; a- f(x) = M, where L ≠ M and either…

Q: Compute f(x +h) + f(x– h)- 2f(x) lim h-0 h2 for the following functions: (a) f(x) =x (b) f(x) = x2…

A: For the real function f, if f(a+h)-f(a)h has a limit, h approaches to zero. This limit is the…

Q: |2²–16| a) Evaluate lim using table of T-4 functional value. ах — b, X<1 b) If f(x) = { x? 13x<5 is…

A: Explanation of the answer is as follows

Q: 1 Let f(x) = 1, 0sx<2 -x2 + 4x- 3, x22 . Compute lim f(x).

A: Topic -limits

Q: 1. Show that for all f e L'(R) lim %3D

A: Put the delta = 1 in integral function

Q: Consider the function f(x) whose graph is f(5) %3D 6. lim f(x) 4 lim f(x) %3D エ→5 3 lim f(x) 20 I-3+…

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Q: 3].. Use € Use e – 8 definition of a limit of function to show that: 2x = 1. x→1 1 + x a) lim X- b)…

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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: 1 Let f(x) According to the definition, 7 4x f'(x) = lim h0 (Enter the limit in reduced form) %3D

A: Givenf(x)=14x-7

Q: 1 Let f(x) =. 1,0sx<2 .Determine lim f(x) -x² + 4x – 3, x 22 X2+

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Q: 2. Let f be defined by the equation f(x) = V3-x. a. Evaluate lim f(x) %3D x-3+

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Q: 2. Let x+1 r -1 Determine if lim f(x) exists. r-1

A: The objective is to determine if the limit exists or not.

Q: use the definition of differentiability f'(x) = lim- h-0 f(x+h)-f(x) h to For f(x) = %3D 6. (x-1)…

A: fx=x2x-1 Now,…

Q: 1. Complete the table of values to determine the limits of the function. f(x) = = -1-0.5 -0.1 -0.01…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: - Define the function f:R → R by ƒ (x) = x +1 if x 0 and f (0) = 4. Show that lim,-0 f (x) = 1 and f…

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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: 4.3 #31| Sketch the graph of a function that satisfies all of the given conditions: f'(x) > 0 if x #…

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Q: 3. Consider the function f defined below. Inx for 0<xs2 If f(x)={ then lim f(x) is **]x²In 2 for 2…

A: Given:  fx=lnx         for 0&lt;x≤2x2 ln2     for 2&lt;x≤4limx→2 fx=?

Q: 1. Sketch the graph of a function with the given properties. lim f(x) = 2, lim f(x) = -, lim f(x) =…

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Q: 1. Sketch a graph of a function f(x) with the following properties: f(-2) = 0, ƒ(2) = 0, lim_f(x) =…

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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).

A: The given function is ((g(x) - 6) / (t - 1))  As limit t approaches to 4 the value of the function…

Q: 4x + 1 Let f(x) = x-2 (b) Use the precise definition of the limit (i.e. M, 8) to prove that lim f(x)…

A:

Q: 1. Draw the graph of a function f(x) that satisfies the following conditions. f(-2+h) – f(-2) (a) 3)…

A: Given that, a)limh→0f(-2+h)-f(-2)-2+h-(-2)=-1⇒                       f'(-2)=-1 b)f(0)=0 c) f'(0) is…

Q: 13. Let f(x) = mx + b, where m and b are constants. If lim f(x) = -2 and lim f(x) 4, find m and b.…

A: Answer 13 has been provided below

Q: .t 5-1 lim t t → 0

A: By L' hospital rule we solve above limit.

Q: Evaluate the limit t3 – t lim t→1 t2 – 1

A: We have to find the given limit.

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: H Let f(x) = 0 if x=2 x² −1 if x > 2 Determine the two-sided limit lim fƒ(x). x-2

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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…

A: (1) Concept : A function is continuous if the graph of the function is continuous or we can make the…

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

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Q: 16. Sketch the graph of the function that matches the following characteristics: f(0) = 4 f'(0) = 0…

A: given, some condition on the required functions.

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

A:

Q: Suppose that lim, →o(f(x) – 9(x)) = 0 and h(x) is a function with domain R. a) Assume that |h(x) –…

A: We will answer the first question as we only answer one question at a time. Please resubmit the…

Q: 9. Consider the following information about the graph of a continuous function m(x): • lim→-0 m(x) =…

A: Given: The function mx is a continuous function limx→-∞mx=-2 and limx→∞mx=2 The sign of m' and m''…

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

A: