1. Use the graph of the function f to decide whether the value of the given quantity exists. (If an answer does not exist, enter DNE.) 4 3 1 -4 4 6. -1 a) f(-2) b) lim f(x) c) lim f(x) d) f(0) e) f(2) f) lim f(x) g) f(4) h) lim f(x) X->0 X->2 X->4 X-> -2

Q: 4 if x 2 Find the value of c such that lim f(x) exists. x→2

A: Given the piecewise function :

Q: Hello, I am struggling to find the slope of the tangent line for the attached problem. Thanks.

A: To determine the slope of the tangent line using the definition of the slope at x = a.

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: Find the limits from the given graph of f(). -2-1 1 2 3 4 S lim f(x) T0-

A: The graph of the function fx is given as ,

Q: 2. Sketch the graph of a function with the given properties: (a) f(2) = 3 (b) lim f(x) = ∞ (c) lim…

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Q: 1 1 (b) lim x-0 'tan x e* – 1 -

A: =?

Q: 1. Simplify: yl1 1 x1?y,20 2. Identify the vertex of the parabola y = x + 4x + 3. (-2, -1) (-2, 3) O…

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Q: 4 4 x*y lim (x,y)→(0,0) f(x, y) does not exist, where f(x, y) = ow that (x2 + y4)3

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Q: Question 4 Evaluate the following limits: V5x + 2x 4.1 lim Va +9-3 4.2 lim-

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Q: 1² – 1 Choose the best reason that the function f(x) : is discontinuous at a = -1. x +1 A. lim, »a…

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Q: (b) If we keep the first part of the hypothesis of Theorem 5.3.6(L’Hospital’s Rule) the same but we…

A: We have given that;

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: b) Find two functions such that lim, 0 f(x) = 0 lim, 0 g(x) = 0 but lim, 0 f(x)g(x) = 1

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Q: 4. Sketch the graph of a function that satisfies ALL of the following conditions: • D: {x ER | x# 4}…

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Q: Vx-2 lim х+4 х-4

A: To evaluate: limx→4x-2x-4

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: Consider the graph of y=f (x) 5 3 C -5 -4 -3 -2 -1 10 11 -1 Which of the following is true? (A X--3…

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Q: 7. If the line 3x - 5y = 7 is tangent to the graph of f at the point where x = 4 then lim А. B. С. 3…

A: Given line, 3x-5y=7 It can be written as 5y=3x-7  y=35x-75

Q: 7. Because of their connection with secant lines, tangents, and instantaneous rates, limits of the…

A: Answer

Q: Answer the question. 5, x<-1 x = -1 3-x, x2 +1, Wx-2+5, x2 2 2, Given f(x) = %3D -1< xs1 X 1<x<2…

A: Given function f(x)=1x+5, x&lt;-12, x=-13-x, -1&lt;x≤1x2+1, 1&lt;x&lt;2x-2+5, x≥2

Q: In parts (A)-(C), find the indicated quantity for y = f(x) = 5 – x². A) f(- 1)– f(– 2) (-1)-(-2) f(…

A: Given function is y=f(x)=5-x2f(-1)=5-(-1)2=5-1=4f(-2)=5-(-2)2=5-4=1f(-2+h)=5-(-2+h)2=1+4h-h2…

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: Activity 2 1. Show that g(x) = x² + 1 is continuous at x = 1. a. g(x) b. lim g(x) X-1 c. Is the…

A: Given- gx=x2+1 To Show- That the above expression is continuous at x=1.

Q: 1. If f(x) = x² + 4x – 5 and g(x) = x – 1, then lim f(x) equals x→1 g(x) с. -1/6 а. -6 b. 6 d. 1/6

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Q: 8. Calculate the following limits. (*# y + 1) /2r – y - 2 (a) lim (b) lim (2r - y + 4) (a.v)-(0,0) r…

A: given,

Q: 3.1.58 The following limit represents the slope of a curve y = f(x) at the point (a,f(a)). Determine…

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Q: S 10 10 – x – x2 if a 1 Calculate the following limits. Enter "DNE" if the limit does not exist.…

A: fx=10-x-x2if  x≤12x-3if   x&gt;1

Q: (3 + 5y +7{ ) 2+y? 200 + y02 exists if lim r)(0.0)

A: This is a problem of multi variable calculus.

Q: 1. Given that f (x) = -x² + 4x, and a = 2, find f(a + h) – f(a) lim h→0 h Explain the meaning of the…

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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: 1. Use the graph to find the limits In (t + 2) f(t) = 2- -2 2 a) t→0 lim f(t) b) lim f(t) t→-1

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Q: The graph below is the function f(x) -5 -4 -3 -2 -1 lim I → 1- lim z+1+ 4 mort 42 f(1) = -2- -3- -4-…

A: Solution is given below:

Q: 2 3 The graph of the function f is above. At what x= a value(s) in the interval (-2, 5) does a. lim…

A:

Q: Is the discontinuity at x= 0 in the given graph removable? Explain. 101 8- 41 -10-8-6-4 246 8 10…

A: Given, graph of a function having a discontinuity at x=0

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: 1. Consider the given piecewise function f(x), find the limits at the given values. State if the…

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: 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…

A:

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

A: Given the function simple put the value of (-1) and (-2)  find the value of y and put it on that…

Q: 4 6.xy1 Find lim if it exists. (x,y)→(0,0) x² + y8 *

A:

Q: 2. Construct a table of values to investigate the following limits. 2r +1 lim a. 42 I-3 I+3 if z1

A: This is a problem related to the limit and continuity. Limit of the function is exist if right hand…

Q: [6] 1. Find the following limits algebraically. x2+7x+10 Va+v-x A. lim x→-2 B. lim x--16 x+2 x+4 1…

A: A. Compute the limit as follows.…

Q: 7. There is a removable discontinuity at x = 1 and f(1) = 4 8. There is a jump discontinuity at x =…

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Q: 4 14 Find the limit of function f (x,y)=, (x²+y*)° at the point (0,0) through the path 413 a. 0 b. 1…

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Q: 1 f(æ) = x + 2 then f (3+ h) – f (3) lim h0 h is

A: Given:

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: 4 (a) Evaluate lim, 1 (-) (b) Let f(x) = ? – x. Find the value(s) of x if the second derivative f"…

A: Answer

Q: 1.16 Let f(x) = lim_f(x) = H-4 2, 4x + 19, Calculate the following limits. Enter DNE if the limit…

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Q: -12 -10 -8 -6 -4 -2. 4 10 12 nd i) lim f(x) ii) lim f(x) iii) lim f(x) iv) f(-8) X-2 %65 t m

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…