for each positive number X Evaluate lim |

Q: Evaluate the lim x→0 X

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Q: Find lim 1+ (if it exists) X→ 00

A: Solving the problem by finding the limit.

Q: If 4.x 9 <f(x) < x² - 4x + 7 for x 0, find lim f(x).

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Q: 4л — 6, 2 <г -

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Q: Evaluate a* -b* lim - b* x→0 X

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Q: If 0 < a <1, then lim(a)* = x00

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Q: If 4x s g(x) < 2x- 2x2 + 4 for all x, evaluate lim g(x).

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Q: If If(x) < B[ for all x in an interval containing 0, show that lim x?f(x) = 0.

A: if fx≤B⇒fx≤B for all x in an interval containing 0 show that limx→0x2fx=0

Q: Let graph (x) as below: -6 Solution of lim f(x)is.... x→0* O -2 O 3 O -3 O 2

A: Consider the graph of f(x)

Q: Find lim f (x) where 3 -{ * if a+3 if a = 3 f (1r) =

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Q: Find the value of lim f(x), if x→4+ x 4 8х + 3 f(æ) = O 24 O 21 9. 41 37

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Q: is lim (x – 1) csc TX x→1 :Select one 1 .b - T.C 1 - .d

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Q: Define what it means to say that lim g(x) = k.                                              X-&gt;0

A: Given limit expression is limx→∞gx=k.

Q: IF lim h>0 f(5h•1)-F(1) - 10 lim FIND 670 F(h+1)-f(1)

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Q: Find lim [x csc(x)] as x approaches zero.

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Q: If 4x s g(x) s 2x* - 2x2 + 4 for all x, evaluate lim g(x). x-1

A: Given  4X &lt; g(x) &lt; 2x⁴-2x²+4 Now the lowe limit of the function should be equal to 4X because…

Q: Find Lim x→ o" ( x-0

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Q: EX-1 – Evaluate the following limits: x² + 5 -3 2) lim x2 x ²-4

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Q: Find the one-sided limit

A: We need to find right hand limit, limx→0+6-1x3

Q: Show that lim n-&gt;∞ (1 + x/n)^ n = e^x for any x

A: Express (1+ x/n)^n using e in the base

Q: If 2x < g(x) < x – x² + 2 for all x, evaluate lim g(x).

A: To evaluate: The limit limx→1gx. Given: The function is 2x≤gx≤x4-x2+2 for all x. Concept used:…

Q: Use the graph to find each limit of the graph. y 8 --- f(x) 7 3 6. 个 a. lim f(x) エ→3 b. lim f(x) =…

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Q: x+1 if x<4 lim f (x) if f(x) = - |(x- 4)° +3 if x4

A: Given Function f(x) is given . This function is branch function . We are asked to Evaluate its limit…

Q: Evaluate lim (1+x)/x x→0

A: Please see the answer in step 2

Q: Evaluate -5x lim,→0 tan x O -5 O 1 O 5

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Q: Find lim f(x). Im f0) -O x-2" X--2" (2.4) (4.3)

A: solution:-left hand limitlimx→2-f(x)=0

Q: . Evaluate L = lim(x→0) ((1/ex-1)-(1/x))

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Q: If 4x ≤ g(x) ≤ 2x4 − 2x2 + 4 for all x, evaluate lim x→1 g(x).

A: Now,

Q: 3. Evaluate each limit: x'+7x+12 4x а) im b) lim x +2 x+3

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Q: What type of discontinuity is at x = 3, if lim f (x)= o and lim f(x)= oc = 00 x→3 00? x3*

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Q: When lim f(x) exists, it always equals f(a). State whether this statement is true or false. Xa

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Q: Evaluate the limit: lim X-7 X+7. O A) O O B) 1 O C) -o D) +00

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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: If 1 < f(x) < x² + 2x + 2 for all x, find lim f(x). X-1

A: Explained below

Q: Find lim x+x:

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Q: B. Determine if lim f (x) = f (c)

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Q: Find the value of lim [{(x + p) (x + q) (x + r)(x + s)}¹/4 − x] ∞07-X

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Q: Evaluate lim(1+ tan x)r

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Q: for each positive number X Evaluate lim

A: To evalaute: limn→∞1xn-x-n, where x is posotove number.

Q: fx², if x < -5 if x 2 -5 a) Let f(x) Find lim f (x). х —5+

A: given function is f(x)=x2        , if x&lt;-5x3         , if x≥-5 Now x→5+ means the x approaches to…

Q: +8 If f(x) = find lim f(x).

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Q: Find the value of lim f(x), if x→6+ 6х + 5 5а + 6 x < 6 f (æ) = О 17 O 36 60 O11 O 66

A: Limit of the function

Q: Let f(x) be given by x²+1 if x 2 Find lim f (x) X-2

A: Topic = Limits

Q: Evaluate lim where k>0 X-k

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Q: If f(x) = , find lim f(x).

A: Consider the given function, fx=e4x-19x apply limit, limx→∞fx=limx→∞e4x-19x=e4∞-19∞=1-10=00

Q: There is a jump discontinuity at x = 2 and ƒ(2) = 3 %3D

A: There is a jump discontinuity at x=2 and f(2)=3

Q: if xs-1 - 2 if x>-1 Evaluate lim f(x) if f(x) =

A: Given fx=1x          if x≤-1x2-2     if x&gt;-1 WE have to find the value of limx→0fx. LHL As given,…

Q: If 8x s g(x) < 4x4 - 4x2 + 8 for all x, evaluate lim g(x). X→1 1 Enhan

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Q: If lim x) - 2 x-1 x - 1 DNE lim f(x). = 7, evaluate

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