sin(x²-11x+30) Find limx→6 х-6 a. 0 b. 1 с. 7 d. 11 e. None of the above

Q: (а) lim 1-cos() 3x 1/х 1/х (b) lim хе 1/х (Hint: хe x+0"

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Q: ,- 3y sin (4x) - 3y - 2 e sin (4x) Find lim - 4x (х,у)—> (0,0) - 2 e sin (4x) lim - 4x (х,у) — (0,0)…

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Q: a. limr→0 cos(x) b. limx→n

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Q: sin 04) find limx-2n 2x-4n S0 (x²+x+1)* Q5) lim- (r²+1)100

A: In the given question we have to find the limit of the question 4 and question 5. the question 4 is…

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Q: lim (- %D x2 – 2 sinx + 2x - 1 42 30

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Q: Rx+2sinx Q2.a) lim sin (). sec (in 3+x

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

Q: sin 2t lim t- 2t

A: To find:limt→ 0sin2t2t

Q: sin(1 – t) |2 – 2t| (b) [8 marks] lim t+1-

A: this is left hand limit then limit approaches from left side

Q: 1+sin x-cos x Find limx→ а. 0 b. 1 c. +0 d. -00 e. None of the above

A: We will apply L' Hospital rule for indeterminate forms of limit

Q: {) Lim 1-cos Scos2x 7 メー)○ x2

A: Given: limx→01-cosxcos2xx2 for evaluating given limit, we use L hospital's rule according to L…

Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO FO x-5 • lim х-5 х2-25 = 10 FO

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Q: Q 3/ x-sin x A- Find lim,0 1-cos x.

A: Explanation and solutions is given below....

Q: 1) limy-o 2ytan(1/y) sin(r-0²) 2) lim2n 101-Va 2 3) limg-n/2 (n²-482 )sec\ß] tan2x 4) lim T

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Q: e2x - e 2x 3. lim, 0 sinx

A: To evaluate the given limit.limx→0 e2x-e-2xsin x

Q: 1 COS X 13. lim- ズ→0 14. lim e -3x+4 15. lim 4x+7 ー-00

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Q: 4. lim -0 A. -2/2 B. 1 C. 2 h D. Does not exist sin

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Q: lim a sin(1/2),

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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: (sin x)(15x4 – 5x + 8) Let f(x) = 4x Find the value of limr→0 ƒ(x), or state that it does not exist.

A: Given f(x)=sinx(15x4-5x+8)4x

Q: 8 sin (1r) 3. Find lim 5.r

A: In the question we have to find lim x→08sin(4x)5x

Q: lim (-4 0 sin x x

A: Let ,I=limx→ 01sinx-1xTaking cross multilplicationI=limx→ 0x-sinxxsinxI=0-sin(0)0sin(0)I=00Which is…

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: 1-x c) lim- x1 1-Vx 121 sin x d) lim (Hint: Use a calculator to make a table.)

A: c) limx→11-x1-xd) limx→0sin xx

Q: 5. Find the length of the curve x =y? +2} from y =0 to y = 3. In(5x+2). In 3x 6. Solve lim

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Q: Q5:The value of: * sin (5x) lim I-0

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Q: sin 14x 27. Let L = lim х sin e 14x, that L = lim 14- (a) Show, by letting 0 (b) Compute L.

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Q: -5y 2 e sin (- 5x) Find lim 3x (x.y)-(0,0) 2 e-5y sin (- 5x) lim 3x (x.y)-(0,0) (Type an integer or…

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Q: L’Hôpital’s Rule for ∞ /∞ Evaluate the following limits.

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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: 5x² - 3x b. lim 7x² +1 sint? d. lim sin 5x f. lim 0-x

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Q: 10 sin(4x³) 12x8 lim X→0

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

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.