Question 9 1-COSX Find k so that f(x) D 4x2 is continuous at x-0 k, x=0 口 1/2 口 2/5 O 1/8 3/4

Q: Question 19. Obtain the following integral: I = ƒ4 sin'z cos z dz as a function of æ to within an…

A: Given that: I=∫4sin7x.cosxdx           NOTE: As per our answering guidelines, we can only answer 1…

Q: 8. If f(x) = sin-1x, then f(-) is: A. " 2. TC С. 6. 3 В. D. - 3. 6.

A: f(x)=sin-1x

Q: Question 19 Let F(x) -1. √1+t¹ dt for x in (-∞0, ∞o). Find F'(- 5 sin z O F'(x) = -√1 + cos²x O…

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Q: dx Problem 13. (10) Evaluate by making the substitution x = tan u; remember the (x² + 1)2. limits.

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Q: cos(3x) if x1 Let f(x) = if %3D %3D Then f has removable discontinuity at A) x 0. B) x = 1. C) x= 0…

A: From the definition of removal discontinuity, If limx→a-f(x) =limx→a+f(x) ≠f(a) So, for a = 0 It is…

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: (6) Suppose g is a twice differentiable , and f (x) = x?g (sin x). (a) Find f' (x) in terms of g,…

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Q: Question 15: 2 (a) The limit lim 2i 1+ can n 00 i-1 state the values of a and b. (In(2 e (b)…

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Q: Problem 2. Consider the following sequence of functions fn(x) = x" sin(nx), r € [0,1/2], n= 1, 2,…

A: Thee given sequence of functions is                       fn=xn sin(nx),   x∈0, 12,  n=1,2,...

Q: Question 2 [17] 2.1 If f(x;y) = sin(xy) +x* In y, find f., at (0:4). 2.2 Let f(x; y) = arctan y 2+x?…

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Q: Example 14. Given the function S x + a?, f (x) = if x 0, find the real constants a and B s.t. the…

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Q: Question 11 7x-9 22-9 ifz1 Determine if g is continuous on [ 0, 2 ). (Please indicate solutions in…

A: g(x)=7x-9x2-9,if x<-1[2-x],if -1≤x≤1x2-4x+4,if x>1

Q: Question 4. Prove that the Riemann sum T(i + n) lim Cos n-00 n 2=1 can be written as a definite…

A: We prove that the Riemann sumlimn→∞ πn∑i=1ncosπi+nn  can be written asa definite integral ∫π2πfxdx

Q: QUESTION 3: Calculate and interpret the condition numbers of the following functions. a) f(x) = lx-1…

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Q: Question 2 Find the linear approximation of the function at the given point. f(x, v) = 3 sinx - 7…

A: F(x,y)=3 sin x - 7 cos y at ( 0 , π/2)

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: Question 15. Obtain the following integral: I = f 3x' In(2x) dæ as a function of æ to within an…

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Q: Question 2 Consider f(x) = 1/x on (0, 0). Show that for any a e (0, o0), the area of the triangle…

A: 2 Consider              f(x)=1x    on   x∈(0, ∞) For any,  a∈0, ∞ we have to show that the area of…

Q: log, eln 5)(arccos(x)) simplifies to a) arccos(x) b) cos(x) c) None of these O d) 5 arccos(x) O e) 5…

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Q: Question 2 d cos x Find dx In x A. X sin x x In x sin x+cos x x (In x) 1 COs X x In x sin x+cos x D.…

A: To find differentiation  ddxcosxlnx

Q: 7.(a) f(x) tan (In x) + 52 7.(b) f(x) = log2 (tan r) + In (¹)

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Q: Question 16 Determine f(x) so that | cos(In?x) f (x) dx = sin(In²x) + C ... 2ln(x) A) In(x) B 2In(x)…

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Q: Question 20 Let f(x) =cos(3x) & g(x) = e . Which of the following is true. (f+ g)(x) = 2 e2x +…

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Q: Question 15. Obtain the following integral: I = f 3x? In(2x) dx as a function of æ to within an…

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Q: Question 5. Evaluate the indefinite integral 2020 (x) tan 2021 (x) dx. COS“

A: Given :

Q: If f(x) = sin(cos(2x)), then find f' O-1 O -2 O 1 ||

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Q: Question 8 Find f'(a) for f(a) O f'(x) O f'(x) O f'(x) = O f'(x) O f'(x) cos - 1 cos? an cos - cos 2…

A: I am attaching image so that you understand each and every step.

Q: QUESTION 2 Use the definition of differentiability to show that the function f(x, y) = cos(x² + xy)…

A: Given function: fx,y=cosx2+xy Function fx,y is differentiable at x0,y0 if: ∂f∂xx0,y0 and ∂f∂yx0,y0…

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: QUESTION 16 Let f(x) = sin(x) -e*, Po=0, and p, 1, then by Secant method P2 = 0.657614 0.678614…

A: Given that: f(x)=sinx-e-x,       p0=0 and p1=1

Q: Question 3 2 approximate '(x – 5)" dx using Riemann sum, the partition of 4 subintervals To X - each…

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Q: Question 2 Differentiate the following functions (i) If y= e-t sin 4t, prove that +6+2y = 0. (ii)…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS WE ARE ANSWERING ONLY FIRST QUESTION FOR YOU AS PER…

Q: Question 25 Suppose that f is continuous and gʻ(x) = f(x) for all x. Then sin æf(cos x) dx = (a)…

A: 25. We need to evaluate the following integral ∫0π2sinxfcosxdx                            ......(1)…

Q: If f : (-a/6, t/6) –→ R is defined by f(x) = 2* tan(3x) for every x E (-–1/6, t/6), then f'(0) is

A: Given: A function is defined as fx=2xtan3x for x∈-π6,π6 To find the value of f'0.   Differentiate…

Q: Problem 2. Consider the following sequence of functions fn (x) = r" sin(nr), r€ [0,1/2], n =…

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Q: Problem 13. Let the functions f, g, and h be defined as follows: f(x) = { x sin(1/x), for x 0 for…

A: The function f(x) should be differentiable at a point f(a)  if and only if, 1)f(a) exist2)Ltx→af(x)…

Q: If f(x) is continuous and ∫ 2 0 f(x)=dx=6  then evaluate ∫ pi 2 f(2sin θ) cos θ dθ

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Q: e sin a – x lim 10 10 cos x- 10 O - 0.2000 | O 0.1000 O - 0.1000 O 0.2000

A: Use L hospital's rule as it of indefinite form. So differentiate the numerator and denominator both…

Q: Consider (D² + 1)y= se = sec x . If y, = f cos x + g sin x, what is f and g ? A = In cos x|, g = x f…

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Q: Question 2. Find the largest interval of existence and uniqueness of solution for the IVP 1 tx" +…

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Q: e* – 4 , x 3 lim f(x) = O 1 O e - 4 O 1 O DNE

A: Pi value is approx 3.14 which is greater than 3 so f(x) at x=pi is cosx

Q: Question 6 Differentiate: y = arccot (x) + arctan 2 + x 1 - 2x 0 1 (E) None of these O:2x O 1-2x

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Q: QUESTION 4 For the given function f(x) = cosx, let xo 0.2, X1 0.4, and x2 = 0.7. Find the Error…

A: Given - For the given function fx = cosx, let x0 = 0.2, x1 = 0.4, and x2 = 0.7 To find - Find the…

Q: QUESTION 5 10 If continuous and Jx)dx = 54, then which one of the following numbers can take at…

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Q: Question 14. Obtain the following integral I where: [z sin(3=)dz I= as a function of æ, to within an…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Question 170 Calculate f 3 in x.cos x dx. (a) 3sin x cos x , In 3 (b) 3cosx . In 3 (c) 3sin x. In 3…

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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: Question 10 tanx If f(x)= A (B) C D sec ³x Itelin sec²x Iteline 1+1² I+e' -dt, then f'(x) equals…

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Q: 3.3. Consider the functions: f(x) = sin(x – 30°) %3D g(x) = cos x 3.3.1. Write down the period of g.…

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