(a) lim sin 3x x-0 sin? 5x (b) lim x-0 x2 (c) lim tan?x x-0 x2 cos? x - 1 (d) lim x2 cos?7x - 1 (e) lim cos2 x – 1 x-0 x2 (f) lim ズ→0 x2 cos8 x – 1 (g) lim x2 (h) lim cos7 x -cos 15x cos4 x -cos 2x x2 (i) lim x2

Q: x²-4 1) lim х>2 х-2 sin 2x 2) lim x→0 3) lim( X→0`x 5x2-Зх 4) lim X→∞ 7x2+1 d 5) [In|sin x|] - dx d…

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Q: II. INDETERMINATE FORMS COS X X 5. lim x →∞0

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Q: 1 + x + sin x 47. lim 3 cos x 49. lim Vx + 4 cos (x + T)

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

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Q: sin x 3. lim -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x) x-2 4. lim x2+x-6 X-1 0.9 0.99 0.999 1 1.001 1.01…

A: To find limx→0sin(x)x numerically. Find the f(x) values for each x value using function f(x)=sinxx.…

Q: 4 2 dx In evaluating √ √²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x) if…

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Q: Limits involving conjugates Evaluate the following limits

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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A: Given: a)∫011-cos xx2dx b)limx→0ln1+x21-cos x

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Q: e* — х — 1 (a) lim x→0+ x² x – sin(x) - (b) lim x→0+ x3 x2 x3 + 4x? + 4 + 4x (c) lim x→-2 x³ +7x² +…

A: We have to solve given problem:

Q: lim x → ∞ cos(16/x)^(13.32x^2)

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Q: Finding LimitsIn Exercises 15–28, find the limit or explain why it does not exist.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: x-2 2. lim 2 x-8 x+3 5. lim 1/x+1/3 1 8. lim X-1 x-1 11. lim X-0 sin x 14. lim (x-3) cscx

A: We will first discuss the L-Hospitals rule. If the limit of the function is of the following form we…

Q: COs x lim 1 (b) In(2/9) – In(x(1 – x)) x – 2/3 - - lim x→2/3 (c) lim r(tan x2 - In x lim x0+ x In(1+…

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Q: find the one-sided limit

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: i) lim cos x-0 7 πCOS²x x²

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Q: 1 im =1-1=0 sech²x. 0 - 0 = 0 tanhx -x sech?x-1 lim X+0 x-olx sech?x+tanhx )= sech?x-1 lim x tanhx…

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Q: x + 3 6x2 + x - 1 41. lim x-3 x +x – 6 42. lim x→(-1/2)* 4x² - 4x - 3 43. lim 44. lim 6 45. lim x→-4…

A: We will evaluate this limits by using one sided limit as shown below

Q: lim h-0 2h sin(x² )dx = -2h cos(1) sin(1)

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Q: graph each function. Use the graph to find the indicated limit, if it exists.

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Limits at infinity Evaluate the following limits or state thatthey do not exist.

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: (a) lim 1-cos() 3x (b) lim xe 1/x (Hint: xe

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Q: (a) lim r0o In(x² + 5) In(x + 2) (b) lim(1+3 sin x)/ª. 2 cos x - (c) lim r1/4 1- tan x

A: I use L hospital's Rule

Q: (r +1)' sin x (c) lim - 2.x X-0 sin x (d) lim- X-0 20' lim + sin 0 (e) 40

A: According to our guidelines we can answer only three subparts. Kindly repost the otherquestions in…

Q: x 0+ (d) lim (1 – 2x)¯4" -4x x→0+ (e) lim (sin æ)-In æ (f) lim (– In æ)*in æ sin x

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Q: X 1) f(x) = x6 + 4x + 2 I NIX - 3) f(x) = ln(x5 - cos²x) 5) f(x)=xsin x + πT x5 -√x - In 3 3 2)…

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Q: 2x + 5x – 1 x<0 - 17. f(x) = | sin x x 2 0 (a) lim f(x) (c) lim f(x) x0- (b) lim f(x) (d) f(0)

A: The given function is f(x)=2x2+5x-1     x&lt;0sin x                 x≥0

Q: |- lim メ→ X-3 2. lim メ→2 (会 4 メー2 メ*-4 3. lim メ→。 3メ - S;u4X 4. lim メ→。 tau3X 5- lim 1- Cose Sin'e

A: Since you have asked multiple questions. So, we are solving first few for you. If you want any…

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Q: lim x→0 g(x) , where ((1-cos(x))/x) <g(x)<.5e^x-.5 for all x on [− 2 2, ].

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Q: (1) lim (In ) = z (x1 (j) lim rsin z x→0+ sin 2x + 2 arctan 3x + 3x2 (k) lim x→0 In (1+3x + sin? x)…

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Q: #37

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Q: 71. Prove the reduction formula tank x dx = tan" k-1 х | tank-2 x dx k – 1 Hint: tank x = (sec² x –…

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Q: 1 - cos b. lim COS x 1 x0cos x 1 20. a. lim x0COs x 1 a inil ol l

A: Given information:The given limit function is shown below:a)

Q: cos x In (1 + x) a) dx. b) lim 1 - cos x

A: Given: ∫011-cos xx2dx limx→0ln1+x21-cos x

Q: (b) lim (e) lim x-0* V4+ Vx-1 x+sin x (h) lim X0 x+ cOS X x+sinx (k) lim [x] (n) lim X3 X

A: Limits questions

Q: The limit lim (18 x; - 28 sin (x;)) Ax i=1 on the interval 0, is equal Tt/4 | (9 x² + 28 cos (x)) dx…

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Q: Rewrite the following as one-sided limits as in Exercise 50 and evaluate.

A: To evaluate the limit. (a).…

Q: 10. lim ) 1 -1) A-0 hV1+h sin x 13. lim 0 2x-xr V8+x -2 (Hі 16. lim

A: We have to use proper techniques here.

Q: (x+h)³-x³ lim h→0 h. sin(3w) lim w-0 2w sin(h)(1-cos(h)) lim

A: We know (a+b)3 = a3 + 3a2b + 3ab2 + b3 limx→0sin xx = 1 limx→01 - cos xx = 0

Q: 2²+ cos(x) x 0

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Q: cos (x + h) – cos x f'(x) = lim h0 57. h cos x cos h – sin x sin h – cos x lim h sin h cos h = lim (…

A: Given: f'x=limh→0cosx+h-cosxh

Q: Finding LimitsIn Exercises 9–28, find the limit or explain why it does not exist.

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

Q: x² – 9 2. lim x →- 3- x+3 (4 + h)² – 16 4. lim h-0 h sin2x 6. lim t tan³x

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Q: 7) Find lim (tan(2x))/x= evaluate the values of (tan(2x))/x below. ON ==>"Y=" ==> Y1 = tan(2x)/x ==>…

A: The function is tan(2x)x

Q: 2-27 1- lim X-3 2-9 2-2x2+1 2- lim -0 -2 Vx+25-5 3- lim sin2x? 4- lim x-0 x sin x 5- lim X-0 2-2cosx

A: 1.

Q: Limits with trigonometric functions Find the limits in Exercises 43–50.

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Q: 2x +5x-3 1. lim 6x -7x + 2 4x-6x+3 lim 16x +8x-7 4. x'+8 7. lim 2x-16 1 -1) h-0 hV1+h 10. lim ) sin…

A: 1) Here, the direct substitution  of the limit value will lead the denominator of the function to be…