I. Let f(x) = Where r is the last digit of your university ID. Find lim f(x) X-3 Let f (x) = 2x2r+1 II. x+3 Where r is the last digit of your university ID. Find lim f(x) X-3 3-x III. Let f(x) =; 9+x2 show that f(x)is continous IV. Show that the function given below is continuous. 4v2 - 8v lim D2 v- 2 v. Show that x2 – 2x – 3 lim X-3 3-x Is continuous or discontinuous at x = 3

Q: The graph of   f(x) = 2x2/(x2 + 2) is shown.…

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Q: Suppose that lim 4f(x)+ 2x – 14 5. Find lim f(x). z→1 %3D z→1 x – 1

A: Given

Q: Suppose lim

A: We distribute the limits and then plug the given values.

Q: Consider the piece -wise function h): = (x)4 x²-2x +3 for x 2 Find lim hx) Find is h«) Contiouous?…

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Q: Consider f(x)=x−9/x+4 a) As x→∞, f(x)→ b) As x→−∞, f(x)→ f(x)=10x+7/x−6 c)limx→∞f(x)=

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Q: If Зx <f(x) < х +2 for 0 <x< 2, find lim f(x). х—1

A: Result used:

Q: Let f(x) = 3x – 4 and g(x) = 8x² + 2x – 2. What is f(x) limx→-1 g(x) O a. -- Оа. O b. 7 4 1 Ос. 8

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Q: Let f(x) = x² + 9, x > 0. Find lim f'(x) →25

A: f(x)=x2+9

Q: If 2x – 1 < (x) <x² for 0 < x < 3, find lim f(x)

A: The solution of above question is written below.

Q: Determine whether f(x) approaches o or -o as x approaches 5 from the left and from the right. -1…

A: fx=-1x-52=limx→5--1x-52=limh→0-15-h-52=limh→0-1h2=-∞

Q: Find the limits 1 lim as (x – 1)4/3, a. x→0+ b. x→0 c. x→1* d. x→F

A: Given function is fx=1x13-1x-143

Q: If 2x - 1 0, find lim f(x). X→2

A:

Q: ; Be h(x) = - 2x + 1, x + 3 calculate lim h(x) 7,x = 3 x-3

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Q: x2 Given that f(x) where a and b %3D (x- a)(b- x) are natural numbers and a > b, find lim f(x). X-a

A: Givenf(x)=x2x-ab-xwhere a and b are natural numbers and a&gt;b.

Q: Estimate the value of lim 1 + 3x 1 by graphing the function f(x) = x/(/I + 3x – 1).

A: It is given that limx→0x1+3x-1 It is known that if we have limx→af(x)g(x), and after plugging the…

Q: Find lim h(x), if it exists. f(x) = 7x2 + 2x + 3

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Q: If 3x – 1 0, find lim f(x). X→3

A: Given query is to find the indicated limit.

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: (4) Consider the function + 3bx + 262 if x 1 For which value(s) of b does lim f(x) exist? Justify…

A: Given: fx=x2+3bx+2b2             if x&lt;1 fx=x-1                             if x≥1 limx→1fx…

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: Given: f (x) = -3x2 - 1 Find: lim, 1 (f (x))

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Q: 1. Determine the lim f(x) if f(x) : = {x*. if #2 lo, if x = 2 2. Find lim f(x) if f (x) = 2*

A: (1) Given that, f(x) = x2 ; if x is not equal to 2 f(x) = 0 ; if x = 2 Then we get, As x -&gt; 2,…

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)…

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

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Q: Given f(x) = 3/(4-x)3 , evaluate limx=4+ f(x)

A:

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: Find. 1) a. lim f(x) and b. lim f(x). 3- 4-

A: Answer and explanation is given below..

Q: If f(x) = 22 +1, then find lim f(x)-f(0)

A: Given, f(x)=2x2+1 ∴ f(0) = 0+1 = 1

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

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Q: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find x→ -2 p(x). r(x) .…

A: Suppose that limx→-2p(x) = 4, limx→-2r(x) =0, and limx→-2s(x) =-3.

Q: Find limx∞ h(x), if it exists, f(x) = 5x3 − 3…

A: Given: fx=5x3-3

Q: Let f(x) = Vx - 1 if x>4 and f(x) = x² – 4x + 1 if x < 4. Find: %3D lim f(x) x→4

A:

Q: Consider the piecewise function x² +2x- 1, if x < -2 -x +1, if - 2 < x < 1 x² + 1, if x 21 f(x) =…

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Q: find the lim as x approaches infinity when f(x)= (1-x)/2x

A:

Q: If 2x - 2s f(x) S x² - 2x + 2 for x 2 0, find lim f(x) x-2

A: see below the answer

Q: Evaluate lim f(x+h)-f(x) h→0 for the given value of x and function f. h f(x)= 5x , x= -2 |

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Q: Given f(x) = 4 – a² and g(x) = væ + 1, find lim g(f(x) 2

A: Given,     f(x)=4-x2        and     g(x)= x+1then, to find                 limx→1gf(x)=?

Q: Use the graph to compute , lim f(x), x+3 -6 -4 -2 2 2.

A: Find the Limit of the function

Q: Given: fix) =x- 5 and g(x) = 2x a) lim f(x) = X--3

A: Given; f(x) is a polynomial. So f(x) is continuous at every point. Therefore limit at x = (-3) will…

Q: Given the function f(x) = 4x - x + 4, determine: f(z) – f(x) a) lim Z-X

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Q: Use the –δ definition to prove that lim x→1 (3x + 5)/2 = 4.

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Q: -x2 if x 3 Iff (x)

A: Take value of f(x) for value of x just less than zero.

Q: Find lim f(x) X+ 0-

A:

Q: Given f(x)= 5x+1,Find lim (x +h)- f(x) h when x>--? h0

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Q: What is the lim f(x) where f(x) = {x" + 10x+24, if x -3 %3D X-3 A. 0 В. 3 С. 12 D. DNE

A: Given: fx=x2+10x+24, x≤-3-x, x&gt;-3   As we know that; The limit limx→afx exists when the left-hand…

Q: ) Evaluate the function  f(x) =x2   -(2x/1000 )for x=1,0.8,0.6,0.4,0.2,0.1 and 0.05 and guess the…

A: Given function, f(x)=x2-2x1000

Q: What type of discontinuity is at x = 3, if lim f (x)= 0 and lim f (x)= 0? x-3 x>3* What type of…

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

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.