28 + x³ Let h(x)=- x<1 x² –1 x>1 x² + x - 2 a) Find h(1) b) Determine the values of ß if lim h(x)exists c) Using the value of Bobtained in b), show that h(x) is continuous at x = 1.

Q: 8) Evaluate the limits: a. lim x sin X00 ex-x-1 b. lim x3

A: As per the company policy i can answer only first question for you,more than that leads me towards…

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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: 2. Find a formula for f that satisfies the following conditions: lim00 f(x) lim-3- f(x) = 0, 0,…

A: Rational function –          In a rational function we have to find intercepts, asymptotes and end…

Q: II. INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) F(x) f'(x) F'(x) lim = lim…

A: To evaluate the given limit of the function.

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A:

Q: I. INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) f'(x) lim = lim Equation 1…

A:

Q: 9.. Ax)= 2x² +x lím f(x), lim f(x), limf(x), a) Analyze the following limits: x-1 lím f (x) Based on…

A:

Q: 1- cos X lim x→0 1- Prove that

A: As per Bartleby's expert answering policy, we cannot answer more than one question so kindly post…

Q: Use the Squeeze Theorem to show that lim (x2 cos 12rx) = 0. Illustrate by graphing the functions…

A:

Q: 1. Find the intervals on which f (x) = Vx² – 9 is continuous. 2x 2. Either find lim ( -) or use a…

A:

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^-?…

A:

Q: State whether the function f(x) = /x - 12 is continuous at x 8. If it is not continuous, tell why.…

A: The given function is: f(x)=x-12

Q: V. Show that Зx? — 6х — 9 lim 3- х X-3 Is continuous or discontinuous at x = 3

A: A function fx is continuous at x=a if its left-hand limit, right-hand limit and fa are equal and…

Q: 2x+1 if x < 2 Let f(x) = x²-1 if x ≥2 Determine the one-sided limit lim f(x). x 2+

A:

Q: 4. Find the limit, if it exists or show the limit does not exist: a) lim (x,y) (0,0) x + y* .2…

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Q: Determine value for c so that lim f(x) x--> 3 exists f(x)= 1/3x+c    For x3

A:

Q: 1. Find the limit of the function (if exists). If the limit does not exist, explain why. For…

A: find the limits

Q: Prove that lim x → 0+ (√x [1 + sin2( 2π/x )]) = 0 (using the squeeze theorem)

A:

Q: 40. Prove that lim Vx esin(7/x) = 0. 41-46 Find the limit, if it exists. If the lim explain why.

A:

Q: Prove that lim x-&gt;0+ √ x [1 + sin2 (2 π/x)] =0

A: Given: limx→0+x1+sin2 2πx By using the property of limit, the limit of a product is the product of a…

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A:

Q: Given that lim f(x) X+ 0 x2 1- explain why lim f(x)= ∞, x2 +7f(x)- sin (5x)+ 1 2- evaluate the limit…

A: We have to find the following

Q: 1. Find the limits. (Don't use L'hopital Rule) V2h+1-1 a. lim h-0 b. lim_(x – 3) -2| x--2 (x-2)

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 2. State whether lim f (x) and f(c) are equal or unequal at the given value of c. Also, state…

A: Given is the graph of the function. We need to specify whether the limit at given values of x is…

Q: 5. Evaluate the limits using any of the methods you know. Show your work. 1-cos 2x а. lim x-0 4sin2x

A:

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)…

A:

Q: Q/calculate limit statement lim 1-sinx X→ 1/1/20 X2502-1

A: It is not a limit questions we don't have check a+ and a- limit we have to put directly limit

Q: The process by which we determine limits of rational functions appliesequally well to ratios…

A: limx→∞2x53-x13+7x85+3x+x

Q: A function is defined by: In( x- 1) f (x) =- 1-x a) Using L'Hopital's rule, show that: lim f (x) =0,…

A: Critical points

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

A:

Q: 1a. Use L'Hopital's Rule to find the Limit: lim         (xsinx + x2 - 4x2)/x - 2pi x-&gt;2pi

A: Let's understand the L’Hospital’s Rule If where a is any real number, infinity or negative…

Q: 2. Suppose f is a positive function. If lim,»a f(x) = 0 and lim, a g(x) = 0, show that lim [f(x)]•w…

A: limx→afx=0  &amp;  limx→agx=∞

Q: 3. What is lim f(x)? lim f(x)? Why? 10+ 8. 6 4 2- -5 -4 -3 -2 -1 2 3 4 4. What is the limit of lim…

A:

Q: Hon of the Squeeze Theorem) on the same screen. 37. If 4x-9 ((x) x* - 4x + 7 for x> 0, find lim f(x

A: Given: If 4x-9≤f(x)≤x2-4x+7 for x≥0. find limx→4f(x)

Q: 1. Given 2-x 06 a) Do the following limits exists at lim f(x) and lim f(x). b) Does function f…

A: We have to solve the limits.

Q: 4-If. 2-x s flx) < 2Cos(x) for all x then find: lim (x)

A: Given: 2-x≤f(x)≤2 cos(x)

Q: x² +1 Evaluate the limit of limx ( - ax – b) = 0 - x+1

A:

Q: 4. Find the limit, if it exists or show the limit does not exist: a) b) lim 47,² (x,y)(0,0) x + y…

A:

Q: ). Determine the interval(s) on which f(x) =4x−12x−1is continuous. b). Find lim x→0…

A:

Q: 1. Determine if lim f(x) exists or does not exist. f(x) = {6 if x>0 If x < 0 2. Evaluate lim f(x),…

A: Limit at x tends to 0 is not exists because right hand limit is not equal to left hand limit.  Limit…

Q: 1. (a) Evaluate the limit or state that it does not exist: i. lim 32-1 37-1 ii. lim V1+r-VI-x (b)…

A: The limits are required to be solved. Each part is solved in detail below.

Q: 2. a) Find lim g(x), lim g(x) and lim g(x) x→1- x→1+ x→1 b) Find f(1). c) Is g continuous at x = 1?…

A: Follow the procedure given below.

Q: 2xy Show that lim does not (x,y)→(0,0) x² + y² exist.

A: The limit function is limx,y→0,02xyx2+y2

Q: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph…

A:

Q: 1- let f(x)= |x^2-4|/(x+2). Determine the limit lim_{x->-2} f(x), if it exist.

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

Q: 1. Shows that the function f(x): x2+2 Lis continuous at x = 0, but has jump discontinuity at x-3 x=…

A: 1. f(x)=x2+2x-32. f(x)=x2-9x-33. limx→-12x2-ax-14x2-2x-34. f(x)=x2-xx-1

Q: -x + 1,x 2 0 Let f(x) = {x² + sin x -,x <0' (a) Find left-hand and right-hand limits as "x"…

A: Consider the given information: