2k For what value of b does the integral x² dx equal lim E1+: k=1 ? (A) b = 2 only (B) b = 3 only (C) b could be any real number. (D) There is no such value of b.

Q: Q2/ a) If f) = , what are the domain of f(x) and g(x)? sin 6x lim 0 sin 9x b) Find

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Q: Express the limit as a definite integral on the lim 17(x;) - 7x;]Ax, [2, 8' i = 1 dx 12 Need Help?…

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Q: x' - 4x? – 9x+36 lim b) x - x-12 x-3 e* -e* – 2x lim c) x- sin x

A: limx→-3x3-4x2-9x+36x2-x-12=limx→-3x2x-4-9x-4x2-4x+3x-12=limx→-3x2-9x-4xx-4+3x-4=limx→-3x2-32x-4x-4x+…

Q: Q4: A) solve: 1+rsin 1) lim y-0 1+xcos

A: Given: limy→01+xsin1x1+xcos1x

Q: e 3x (d) lim X→0 5x+200

A:

Q: 2+4r+4 If f(x) = why does f(-2) not exist? Show algebraically that lim f(x) %3D X+2 I-2 does exist.…

A: fx=x2+4x+4x+2 take x=-2 f-2=-22+4-2+4-2+2 f-2=-22+4-2+40 here denominator is zero when x=-2 so the…

Q: lim yn2 +n -n=0

A: Limit problem......

Q: lim - 1, avx + 3 – b x - 1 lim If score А. 4 D. В. 2 С. 1 E. -INI14

A:

Q: For n > 0, use Taylor's theorem to find (1+x)!/n – 1 lim 3.

A: Explanation of the answer is as follows

Q: 2n +1 a) Using the definition, show that lim n00 3n +4 3

A: Given,           limn→∞2n+13n+4=23

Q: Q 4. (a). Simplify the indicated limits on the following. 3x2+5 lim x-0 x²+1 + el-*] (i). (ii). lim…

A: 1) =?

Q: (fif2..f)is di fferentiable at x, proofthat ... by using f(x)– f(*.) f (x)=lim, x-x,

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Q: x² – y? - Show that lim (x, y)→(0, 0) x² + y? does not exist. .2

A: Given: lim(x, y)→(0, 0)x2-y2x2+y2

Q: Q27. The value of lim (1+x)5-e5x+sin x² is? e x2

A: The given limit,limx→01+x5-e5x+sinx2x2

Q: 4.x 2x 7e lim 1- e4x

A: We have to find limx→∞ e4x-7e2x1-e4x.

Q: 3. Find the values of the constants a and b such that Va + bx – V3 - lim x → 0 3.

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Q: lim Vn² +n –n=0 -

A: Given Lim n-infinity √(n²+n) -n When we pit n is infinity directly we found a infinity-infinity form…

Q: (a) lim x→2 arctan(7-3x)-" 2х-4 4 (b) 10-e5x lim x→00 16-x2

A: See the calculation and explanation below

Q: 4. lim x5 x- Note* the sign is negative -1/2 5. lim va N. -- I. 2v2 6. lim 3x Vx Н. 243 3 x-27

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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: Find lim 1+1? 1-e24 -2t -1 tant, 2 2 1-1

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Q: lim is x-0 X O A. 0 О в. 1 C. 8.

A: B. 1

Q: 54. Let L = lim 9L is equal to 2e e then the value of L= 2e2 3. and Imactting

A:

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…

Q: (iv) Find lim r 2ª – x² sin

A: Limits

Q: 4x e lim x→0 r2

A: The series expansion of ex is ex=1+x1!+x22!+x33!+x44!+...

Q: O3: A- Find the limit for the follo tan2x 1- lim x→0 sin4x

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

Q: e – e-* lim I-0 x2 + 3T

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Q: tan(xy) = ? lim .2. (х.у) >(0,1) х*у+x 1 1 (b) 1 (e) (d) - (а) 0 (e) 1 4 - |3

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Q: Q3 Find the area inside one leaf of the three leaved rose r-cos30 (upper lim and lower limit= n/6)

A: Given: The value of r and the value of θ. To find: Area inside of 1 loop. As per policy guidelines,…

Q: 16-2 Evaluate: lim +4 V12+-a dne O 2 12 3 14

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Q: (b) lim (r + 1) In x

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Q: 1 d) limy-→0- e) lim,o (1+ r/n)" 1 f) lim→0 x +

A: L'Hospital Rule : If limx→af(x)g(x) is in the form 00 or ∞∞, then limx→af(x)g(x) = limx→af'(x)g'(x)

Q: 3x²+2x+1 Q1: Using the L Hopital Rule Evaluate: lim x→0o 5x2+3x+3

A: Given: limx→∞3x2+2x+15x2+3x+3  ……1

Q: x - 2x What is wrong with applying L'Hôpital's Rule to lim x+0 3x – 2

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Q: nx + 1 If lim エ→+0 = 9, find n. 1 %3D nx -

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Q: (c) lim r³/x² 3/22

A: We have to find the limit value by using L'Hospital rule.

Q: V2x(x-1) 3. lim-1 Jx-1|

A: Given limit, limx→12xx-1x-1

Q: Q27. The value of lim x-0 (1+x)5-e5x+sin x² x2 is? →

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Q: x+1 If f(x) = Solve to find lim f(x)? %3D Vx2+5-x'

A: Here is complete computation for your limit

Q: 8. Find the area of the triangle formed by the x and y-axes and the tangent to the graph of y =. %3D…

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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: b. lim X-0* e -3/x 2 X²

A: Please see the attachment

Q: V4 - x2 0sx<2 lim f(x), where f(x) = < 2 9) x-4" 2 sx<4 x = 4 B) Does not exist A) 4 C) 2 D) 0

A: f(x)=4-x20≤x&lt;222≤x&lt;44x=4

Q: 3+2r lim エ→0 =?

A: Given , limx→03x2+2xx

Q: b-4+ Jb 3x(x – 4) Answer "True" or "False" for the following: In(x – 1) Ji 3x(x – 4) In(x – 1) |…

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Q: 2n2 + n (a) Using the definition (i.e. N, ), prove that lim 4n2 2 112

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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

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.