3. Suppose lim,-c f(x) = 5 and lim,c g(x) = -2 a. lim f(x)g(x) b. lim 2f(x)g(x) f(x)

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

A: Given the piecewise function :

Q: Find the limit for when x -> 4 lim F(x), for f(x)= x2+2 ; x≠4 ; 27; x=4

A:

Q: Find the limits lim х2 — 1 as a. x→1+ b. x→1 c. x→-1+ d. x→-1

A: we have to find the limit    the given expression is

Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

A:

Q: 2) Show that the_lim. 1) xy2 lim (x,y)→(0,0) x² +y²

A:

Q: (-금x+ 2, x 0 exist? If yes, give its value. If not, why?

A:

Q: 21 f(x)= 3x2 +4x +1 and g(x) = x2 -2x-3, then what is lim f(x) *→19(x)?

A:

Q: 1. Use the definition to show that x² - y² lim (x,y)→(0,0) x² - y² = 0.

A:

Q: lim[f(x)+ 4g(x)]

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Q: Determine the value for c so that lim f(x) exists. X-4 x2 - 9, for x4 The value of c is

A:

Q: If lim g(x) = 10 and lim h(x) = 28 then x5 x5 lim [2g(x)+ 5h(æ)] x5

A: Solution to the first question: Given,            limx→5g(x) = 10  and limx→5h(x) =28

Q: Find lim x^2 − 3x + 2/x^3 − 2x^2 as (a) x → 0+ (b) x → 2+ (c) x → 2−

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: 43. Assuming that lim 4 = 1, which of the following statements is necessarily true? Why? (a) f(0) =…

A: Consider a f0=0Here if x=0 , f0=0Substituting in limx→0fxx=00Inderterminant formDifferentiate…

Q: Find lim,-1 f(x) -3 -2 -1 2 O lim,→-1 f(x) = 2 O lim,-1 f(x) = 1 O lim,-1f(x) = -1 Lx→-1 f(x) = –1 O…

A:

Q: 39. Find lim f(x) if, for x > 0, 4x? – 5 4x6 + 3 - < f(x) < x6 x2

A:

Q: Suppose that on the interval (2,5) f(x) less than or equal to g (x) less or equal to h (x) and Lim…

A: We have the following information.

Q: Q2 e valuat of the fallowing 2. ☺ lim L(x +3)t -16] xーース ☺ lim -25 X+5 メー5 lim |-X 3+X 9. X-3 メー] O…

A: To evaluate the given limits.

Q: Given: x + 1, -2 < x < 0 x = 0 0 < x < 2 x = 2 2, f(x) = -x, 0, 2 < x < 4 х — 4, What is the lim…

A: Consider the given function. fx=x+1,          -2&lt;x&lt;02,                x=0-x,…

Q: 22. If lim f(x) = 18 and lim g(x) = -1.5, find the lim %3D %3D x-a L4g(x). xa А. 6 -3 С. -1 D. -7 В.

A: 22) If limx→afx=18 and limx→agx=-1.5 , find the limx→afx4gx

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

A:

Q: 12. Given f(x)=x² – 4x – 5. Find lim fx) –{2) x-2 2

A:

Q: Suppose that a function f(x) is defined for all real values of x except at r = c. Does it imply the…

A: Here we have to check whether the limit exists or not.

Q: Suppose that g(x) s f(x) < h(x) for all x + 2 and suppose that lim g(x) = lim h(x) = -5. X-2 X-2 Can…

A: It is given that gx≤fx≤hx and limx→2gx=limx→2hx=-5.

Q: 21. The cost of manufacturing a particular videotape (in dollars) is C(x)=15,000+ 45x , where x is…

A: cost function C(x)=15,000+45 x

Q: For f(x) = the square root of 7x+30, how can I find f’(x) using the definition f’(x) = lim as h—>0…

A: Given,          The function is fx=7x+30.We know that,          The derivative of the function is fx…

Q: Q1/ Find the following 1. lim x2 + 1 = 2 x00 (x-2)2 2. lim x-2 (x-2)(x+2) 3. lim (5 -) x-0

A:

Q: 16. If f(x) = 2x – 1, what is lim x+h h B. - С. —2 D. 2 NIN

A:

Q: If 3x s f(x) sx +2 for 0sxs 2, evaluate lim f(x).

A:

Q: 8-3x, for x <1 For parts b) and c), let f(x)= %3D x+x, for x21' b) lim f(x) x→1

A: We have to evaluate  limx→1- f(x) For x &lt;1 , f(x) = 8 - 3x

Q: 5. If lim f(x) = 8 but lim f(x) does not exist, what can you X+2+ X+2 say about lim f(x)? X2-

A: We know that, limx→afx=l, if: limx→a+fx=limx→a-fx=l

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: If f(x) = 3x2 - 4x +1 and g(x) = x² + 2x - 3, then what is lim 9X, g(x). X-1 f(x)

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Q: Suppose a is a constant and if x>3 f(x) = { if 2 <x<3 %3D x+a if x < 2. () Find lim f(x). X2+ (ii)…

A:

Q: If 5-4x sf(x)s5-x for - 1<xs1, find lim f(x), lim f(x)%= f(x) =D

A:

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: Suppose that following is true. x2 + 6 if x s 0 if 0 <x < 1 f(x): 7x² - 6 if x 2 1 What is lim f(x),…

A: Just compute right hand limit and left hand limit and see if they are equal or not.

Q: 3. If f (x) = (x² – 1, if x 3 3.a) lim f(x) X-3 3.b) lim f (x) 3.c) lim f (x) X-1

A: The given function is f(x)=x2-1,if x&lt;3x+5,if x≥3

Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

Q: 28. Assuming that lim f(x) = 4, compute: 1 (b) lim x+6 f(x) (a) lim f(x)² (c) lim x/f(x)

A: limx-&gt;6f(x)=4

Q: Suppose that f(x) = 2cos (n/3 x) and the graph of g(x) is given by: y = g(x) 2 1 -5 -4 i ż 3 4 5 x…

A:

Q: Given f(x) = 2x^2 + x -15 all divided by x+3 find lim x -> -3^f(x) algebraically is f(x) continous…

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Q: (3х + 3с if x >2 Let f(x) = {x2 - cx if x < 2 If lim f (x) exists, find the value of c. X-2

A: Limit of a function exist , when both sided LHL and RHL exist.

Q: Suppose limy-e- f(x) = I and limx-e- g(x) = m. Prove that limxe-(3f (x) + 4g(x)) = 31 + 4m.

A:

Q: Determine the value for c so that lim f(x) exists. X-3 f(x) = +c, for x3 The value of c is.

A: Topic = Limits

Q: 3. Show algebraically that lim x* – 2 – x = 0

A:

Q: Suppose f(x) = x2 if x ̸= 2 and is undefined at x = 2. The domain is (−∞,2)∪(2,∞). Find lim f (x).…

A: The limit exists at x tends to 2 for f(x). First of all, consider the condition for the limit to…

Q: for g(x)=5 and h(x)=2x find lim

A:

Q: Consider the function - x2, x+1 f(x) = 2, x = 1 O Graph the function f(x). O Find lim,1-f(x) and…

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Q: f(x) is discontinuous at x=c, then  limx→c-  f(x) ≠ limx→c+ f(x) True or False?

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Q: Suppose that following is true. (x2 + 5 f(x) = {x (6x² - 5 if x s0 if 0 < x < 1 if x 21 What is lim…

A: To check the existence of function at x = 1 We will calculate LHL and RHL if they are equal them…

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.