What is the value of x2 -9 lim a-0 x2 x - 6 -3/2 O 2/3 3/2 O DNE

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

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A: To find the limit  limx→-∞xcos-3x

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A: The limit x→a+ implies x  approaches a from the right. The limit x→a- implies x  approaches a from…

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Q: 3. lim Vx+3x + 6 X-2 -1.9 -2.1 -2.01 -2.001 -2 -1.999 -1.99 fx) . lim X--2 x+3x + 6 =

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Q: lim,-«G)* + x²+4 ()* limx--o %D 3x +1 a. -1 1 c. -3 Od. 3.

A: Given, limx→-∞53x+9x2+43x+1  We have to evaluate the limit.

Q: 48. If L = lim (cosec x)/(x, then the value of nL is - X->0* (A)1 (BY-1 (C) 0 (D) none of these

A: To evaluate: L=limx→0+ (cosec⁡x)1/ln⁡x Taking ln both sides, we will get ln L=lnlimx→0+…

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A: We need to calculate the right hand limit at x=2 of the given function.

Q: 1 + cos(x) a) lim %3D 20 -x ) lim x-1( In(61x-60)

A: Given, limx->π (1+ cos (x))/(6(x-π)²) = (1/6)limx->π (1+ cos (x))/((x-π)²) = (1/6)limx->π…

Q: 2sin x lim -0 e - 1 lim - 5 cos x o e - x - 1 4 - 4e* lim -0 xe

A: As per our guidelines, we are allowed to answer the first question only please resubmit the other…

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Q: 6.The lim x +3 is equal to 1S 3x-4x+n sin t. 7.The [1 is equal to

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

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Q: (iv) Find lim r 2ª – x² sin

A: Limits

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A: limx→ 0tan3xln1+xApplying L'Hopital rule=limx→ 0sec23x· 311+xPut x=0=sec23· 0· 311+0=3

Q: 8. Evaluate e8x - 1 lim sin (6x)

A: See the attachment.

Q: Vx? +12 - 4 x²-5x +6 2x-5x +6 a- Lim cos x b- Lim c- Lim d- Lim x - 2 x'-8 3x -8 --

A: If in limit denominator and numerator forms 0 by 0 use L hospital rule

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A: Here we have lim(x,y)→(4,16)x2+xy-2yx-y

Q: If 7- 4x s g(x) s7 cos x for all x, find lim g(x). lim g(x) = X-0 (Type an integer or a simplified…

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Q: x-1 lim when x 2,1.5,1.1_ Q.1. Make a guess about the r->1 X O 99 0 999

A: The expression limx→af(x) will give us the value of f(x) as x approaches a. We know that,…

Q: 1. lim (2r + 5) 2. lim (10 3x) X12 3. lim(-x + 5xr 2) 4. im (x'-2r? + 4x + 8) 5. lim 8(t - 5)(t-7)…

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Q: x.2* 15. lim x-0 2*-1 (A) In 2 (В) 1 (С) 2 1 (D) 1n 2

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Q: (a) Find the following: x1/3 + 9x1/5 (2х — 1)4/2 — 3 х — 5 i. Lim х-о бх1/2 — 4х1/4 ii. Lim X-5+

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Q: Question 10 X-2 lim (- x-1 x+4x-3' O A 00 OB. 1 OPNone of the above is correct OD.

A: We have to find the limit.

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A: We have to find the limit of the expression limx→-7x+7x2+5x-14=?

Q: In cos 2.x 4. Find lim -0 In cos 3x

A: limx→0ln (cos 2x)ln(cos 3x)Applying L'hospital rule:= limx→0ddxln(cos 2x)ddxln(cos 3x)= limx→0…

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Q: (a) (i) Lim  5x −3 − 4/ 2x −2 + 9  x→∞  (ii) Lim      (x − 3) 2/x2/2  − 2x − 3      x→∞

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Q: 2 – 1 | lim X→-1 elx+1)² – 1 | - 1

A: When limit is of the form 00 or ∞∞, then L'Hospital rule is used.In this rule, take the derivative…

Q: 1/lim x²-2k tl X-X 2//im X2+8 72

A: Here given (1) as L=limx→1x2-2x+1x2-x    =limx→1x-12xx-1    =limx→1x-1x    =01=0

Q: 22) Find lim -5 e-2x+6 .given e =2.7 and e0 = 1. = %3D X 3 A) -13. 5 В) - 2.7 C) 0. 0 D) -5.0

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Q: 7. *Find the values of a and b lim sin(ax-2a) x-2 = 3 %3D x-2

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Q: [x-al (a>o) Lim x+ 80a - la 2

A: From the given problem: limx→a-x-ax2+80a2-9a