b ax + x2 Evaluate lim where a>0

Q: Q5/B: Evaluate lim (). x→1/2 \4-x²

A: Recall: limx→a f(x) exists and equal to L if and only if limx→a- f(x) =limx→a+f(x) exists and both…

Q: d) lim g(x), where g(x) = x-2 ~ (x-3)² if x > 2 x+1 if x ≤ 2

A:

Q: If lim f(x) = 11 and lim g(x) = 30 then lim[4f(x)g(x) – 5] = %3D O 1315

A: To solve limx→94f(x)g(x)-5, use the difference rule of limits, limx→ca(x)-b(x)=limx→ca(x)-limx→cb(x)…

Q: ー2 a) lim X >6 (x-6)3 b) lim E) ゼ+t

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Q: Vx+8-3 Evaluate ' lim-1 x+1

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Q: y e 1. Evaluate lim x0 x* + y

A: Evaluate the limit of the function x2y/(x4+y2) when x and h tends to 0.

Q: 2x + 3 Let f(x) Find lim f'(x) x + 4

A: Given function is fx=2x+3x+4. To find: limx→5f-1x Solution: Given function can be written as:…

Q: b. lim x->0+ -3/x 2 X²

A: A limit is a value that a function approaches as the input approaches some value. Limits are…

Q: x² – 9 (b) lim x→3- x + 3

A:

Q: h(x)-h(1) 6. If h(x)=- J4-x² , evaluate lim x>1* x-1

A:

Q: V 19 - x - 4 Evaluate lim X-3 V28 - x - 5

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Q: x² - 7x y +12y Evaluate lim(x,y)→(3,1) х- Зу

A: The given expression is limx,y→3,1x2-7xy+12y2x-3y

Q: If lim f(x) = 12 and lim g(x) = 28 then lim[3f(r)g(r) – 8] = T-4 O 260 1000

A:

Q: Limits of linear functions Evaluate the following limits.

A: Consider the given:  Find the limits: fx=12x−7limx→3fx=limx→312x−7=123−7=32−7=3−142=−112

Q: x² – 1 if x -1 |

A:

Q: 3. y = f(x) 4 6. -1 lim f(x) =

A:

Q: 1. 2. b. f(-1)= b._lim_f(x) = c. lim f(x)= 3.

A: 1(a). f(-1)= -2 1(b) lim x-> -1- f(x)=  -3.5

Q: 2x + 1 Let f(x) Find lim f(x) %3D x - 1

A: Given functionf(x)=2x+1x-1

Q: x2+2x – 3 if x 22 The value of lim f(x) if f (x) =- 6-x X-2 if x<2

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Q: x²-1 X If lim x0 x+1 - ax - b} = 2, Find the values of a and b.

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Q: Give precise definitions of the following statements.

A: Given: a.limx→2-fx=5b.limx→2-fx=5c.limx→2fx=∞

Q: S 3x + 2 x² + 3x – 1 I-2 |

A: Given that: f(x)=3x+2            x&lt;-2x2+3x-1   x≥-2

Q: 1 (B). Evaluate lim (3 – x) x-2 x→2

A: Given that  lim x to 2 (3-x)^(1/(x-2))

Q: 6. If f(z) = 4 then lim f(x)- 12

A: Using limit ,

Q: lim tkx'-1 k is a constant ト

A:

Q: ( ) Evaluate L = lim x+ Vx² + 1 r -00

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Q: f(x) 80. If lim x→-2 x? 1, find f(x) b. lim x2 (x) х

A: 80. Given:

Q: 3(r-4) Vx+5 x-4 3-Vx+5 To evaluate: The value of lim

A:

Q: x² - 1 if x 2 x→2* а) 4 b) – 3 с) 3 d) – 4

A: Given function is  g(x) = x2-1   if x≤2x+2    if  x &gt;2 the function is defined in two intervals.…

Q: 2. a. b. C. f(0) = lim f(x)= x-0+ lim f(x) =

A:

Q: Evaluate the following limits.

A: We have to evaluate the limit: limx→0ax-bxx It is 00 form. We know the formula, limx→0ax-1x=lna So…

Q: f(x)-f(1)_3, then lim ¸ƒ(1+h)−ƒ(1) _3. x-1 h If lim: (a) (b) TRUE FALSE

A: Solution of given question is written in below steps.

Q: 7- x2 if x 2 Iff (x) find lim f (x). I→-1+ |

A:

Q: fa)- 0. f(x)=0 and lim g&)=O then lim メ-0 %3D If lim Xa gG) メ→a True O False

A: Solution: The objective is to prove the given statement

Q: x² +2 if 03 a. lim f(x) b. lim f(x)

A: Function f(x) = x2+2 if 0≤x≤3 and f(x) = 2x+5 if x&gt;3 To find lim x→3− f(x) lim x→3+ f(x)

Q: 2x-1 if x2

A:

Q: b. Evaluate lim X0 ex

A: Given limit is : limx→0xex  To find the value of the limit.

Q: f(x) 82. If lim x→0 x2 1, find f(x) b. lim a. lim f(x)

A:

Q: If lim f(x)= 0, then lim 1 f(z) = +00. I→+00 O True False

A: False This can or cannot be true. please find the explanation in next step.

Q: Va-2x Let f(x) = Find lim f(x)? x+1 +x-

A: Given function :

Q: Evaluate lim f(x+h)-f(x) h-0 where f(x) = 2 – 3x². h None of these -X 6x O -6x O 3x

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Q: x² + 4 Find Lim x-0 ex + 1' A. 2 В. Оо С. 1 D. 4

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Q: a* - b* lim for positive constants a and b

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Q: f(x) – 9 If lim X→1 X-1 =D4, evaluate lim f(x). X→1

A: Given: We have to determine the value of limx→1fx

Q: (3 if x2 If f(x) = - then lim f(x) = 3 X+ 2 A True B False

A: Here we have to find limit of given function.

Q: 8(x) x -1 Find lim

A: Solution is given below

Q: 3 if xs2 x if x>2 If f(x) = then lim f(x) = 3 x-2 A) True B) False

A:

Q: 3) Find lim f(x) and lim f(x) x-(-1)- x-(-1)* -4 A) -2; -7 B) –7; -5 C) -7; -2 D) -5; -2

A:

Q: Find the shown limits:

A: Explanation: Given that,  f(x)=2x+3x+4