Q 9 Prove that sin r is continuous by proving that limn0 sin(a + h) = sin(a) Va ER. (HINT: use sin x addition of angles formula). %3D . Q 8 Find all points (if any) where the tangent to p(x) = x³ – 6x2 +9x – 50 is horizontal 3D%D -

Q: Given the first order IVP y' + 3y = 0, with initial condition y(0) = 5. %3D I >1 (1) Find the…

A: Here we have, y'+3y=3x2e-3x,0≤x<10,x≥1 with initial condition y(0)=5

Q: Question 7 In evaluating 4 2 dx X√√x²-4 s-¹(f(x)). Determine the value of f(x) if x=0.35 is same as…

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Q: - 1 X If lim ([sin ¹x] + [2²sin ¹' (2x)] + [3³ sin-¹ (30)] x →0 X X + [x²³sin-¹ (x2x)]) + ... +…

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Q: Can you please answer this question and show all of the steps and say the correct letter

A: Consider the limit

Q: Consider the function fix) sin x. Complete the table below and sketch its graph. x011/6 11/2 5n/6…

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Q: Which of the following is not true? A Sin(x²)dx= limin(x²)dx c (B) None of the given choices .5 dx ©…

A: Given:  A)∫0elnx2dx=limc→0+∫celnx2dx B) None of the given choices C) ∫05dx25-x2=limc→5-∫0cdx25-x2 D)…

Q: tan (3r) 1+ (3x) 24(V9+x-3) r>0 k I = 0. E the following statements is true about y of the function…

A: We have to choose the correct answer from the given option

Q: s) For f(x) = dy find dx using the definition, 24x dy Ay = lim Ax-0 Ax f(x+Ax) – f(x) = lim dx Ax-0…

A:

Q: Which of the following may be solved by a direct application of L'Hopital's rule? sin 2x lim x→0-…

A: We have to check

Q: S cos (z +1) z<-1 -1<z Let F (x) : e -1 Then lim F (1) =

A:

Q: 2. Given *(t) = (V2 – t, (e* – 1)/t, In(t + 1)) a. Find the domain of * b. Find dř(t) dt c. Find lim…

A: we have been given the vector r→(t)=(2-t,(et-1)t,ln(t+1))

Q: Which of the following is not true? (A) None of the given choices 3 dx dx Ⓒ = S B S³ = In(x²) lim c→…

A: An integral assigns numbers to functions in a way that describes displacement, area, volume, and…

Q: Question 7 Determine if h (z) = –- is continuous at x = 1. (Show your solution at your bond paper.)…

A: hx=x-1x2-1

Q: (b)Consider the piecewise function S (1+ æ)ª – 1, if x>0 = (x) 6 I sin (4x), if æ < 0. Discover…

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Q: E Q4) Evaluate cach of the following: 1- Prove lim sin3xcot5x X-0 xcot4x 2- Find dx Zx+3/ 3- Find…

A: Questiion 1,Given,            limx→0sin3xcot5xxcot4x=125To find : To prove the limit.

Q: In evaluating 2 2 dx XV is same as evaluating lim_ cos-¹(f(x)). Determine the value of f(x) if x=2.9…

A: As per the question we are given a definite integral and we have to find the primitive of the…

Q: 2) Use the figure to give approximate values for the following (if they exist). Enter your answer as…

A: The above figure shows the graph of function f(x), find the following: (a) f(1)(b) lim f(x)x→1(c)…

Q: b. b-a Use the equation fte)dx = lim ** ) to evaluate the following definite integral. n-0k=1 2 |(2x…

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Q: 4 35₂² In evaluating 2 dx x√√x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

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Q: 2x? — х — 1 lim b) х--1 4 — 3x? — х x² + 3x +1 lim x→-1 2x? – 3x – 5 а) VE- 2 m³ – 8m + 1 lim lim -…

A: e)

Q: d) S x?cos (x) dx 2 a) Find f' given that f(x) = cos' (3x+1) %3D sin3x-sin 6x b) Evaluate lim x-+0

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Q: Which of the following is equal to lim h→0 Old + 1/1/12 2 dx +=h { (20²2 +20)] - [2²] + d [1 dx da 2…

A: This is a problem related to differentiation. Based on the definition of differentiation we will…

Q: 1) 土七 COS ant5 Sinant3 an: 2then fird the m lim 3) D. Ehmit does not exist

A: Given query is to find the limit of the expression.

Q: 2 dx 5, is same as evaluating lim cos C+2+ F(<x))". Determine the value of f(x) if x=3.22 In…

A:

Q: 1/a (e) lim (1– sin(z))/=

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

Q: Q2. Let f:R→ R be a function such that f(x) = x sin (-) has a limit at xo + 0. If f is defined at xo…

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Q: (a) Evaluate h(x) tan(x) - x for x = 1, 0.5, 0.1, 0.05, 0.01, 0.005. (Round your answers to six…

A: let fx be a function defined on an interval  that contains x=a, except possibly at x=a. then  we say…

Q: 1 x" cos (nx)dx 1+n? Evaluate lim

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Q: If ƒ is continuous everywhere and 1| f(x) dx = 6, find | sec? 2x · f(tan 2r) dr.

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Q: Find the value of b such that the limit of the function f(x) = cot 2x)(sin bx) as x goes to zero…

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Q: (2+) ( 29 3 7. Suppose that lim In .Fill in the boxes for the corresponding equation involving the…

A: 7.  limn→∞∑i=1n2+3in2+3in2+4.3n=12ln268

Q: - Using any results from the course material, find the following limits: sin(x? – 9) а. lim x-3 (x2…

A: Solution:-

Q: 3. (a) Let f be differentiable on an open interval I and suppose f"(x) = 0 for every x in 1. Show…

A: Let f be a differentiable on an open interval I i.e. (a,b), Suppose that f'(x)=0 for every x in…

Q: 2) Use the figure to give approximate values for the following (if they exist). Enter your answer as…

A:

Q: Which of the following is not true? A √ in(x²) dx = lim_ sin(x²) dx 3 3 dx dx Ⓒ 1² B In(x²) - = lim…

A: Solution is done in step 2

Q: Q2) A: If u = sin-()+ tan-(), prove that du ди x=+y дх ду = 0 ax ay n lim (1+ (1 + iV3)10 B: Find:…

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Q: 6. If f is continuous and f² f(x) dx = 6, evaluate S/² f (2 sin 0) cos de.

A: It is given that if f is continuous and ∫02f(x)dx =6 The objective is to evaluate ∫0π2f2Sin θcos θ…

Q: a) If n is a positive integer, prove as given in image (b) Find a formula for the derivative of y…

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Q: (k sin x + x2, c. For what value of k and m will the function g(x) = . x + 2, be continuous on m In…

A: Given:⇒g(x)=ksinx+x2,0≤x&lt;π4x+2,  π4≤x&lt;emlnex,e&lt;x≤2π A function is continuous at a point if…

Q: 1. The range of y=-e* +2 is (-0,1). 2. The function f(x)=sin x+cos x is an odd function. 3. lim

A: Topic:- function  Topic:- as per our guideline only first three subparts need to be answered.

Q: Q2. Let f(x) - In(cos x) (i) Find the are length (ds) of the function

A: Given,                f(x) = ln(cos x) ⇒y=ln(cos x) ⇒ dydx=-sin(x)cos(x). And we have to find arc…

Q: (E) f is defined at xo , where the value of 8 exactly is Q2. Let f:R → R be a function such that…

A: Q2. It is given that,f(x)=xsin(1x) has a limit at x0 not equal to 0.

Q: 3 2 10) Find the arc length of f(x) = x3 + 10 On [0,8].

A: To find the length of the arc for the given function f(x)=32x23+10 on the interval [0, 8]

Q: a) Complete the table below given f(x)=sin(3x)/x Round your answers to six decimal…

A: Compute the table for f(x)=sin(3x)x

Q: 43. lim (sin t) (In t) t0+

A:

Q: In evaluating 4 2 dx X√ X²-4 is same as evaluating lim cos ¹(f(x)). Determine the value of f(x) if…

A: We have to find the value of f(x).

Q: Which of the following is not true? Ⓒ √ 4dx √x(x+6) c lim dx ⒸS₁² 25² + x² ² m 25-x2 B dx c-5-0…

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Q: 4 2 dx : 5₂² In evaluating is same as evaluating lim cos-¹(f(x)). Determine the value of f(x) if…

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Q: Let f (x) = In (x?) find the equati on oE the line tangent to the graphof f at (3, In(9)) (2) Find…

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Q: d Prove, through the limit process, that (cos x) = - sin x. dx

A: