Question 5 If f is defined on the interval (9, 12], then L" f(x)dx = *f (x)dx – fii°f (x)dx 12 a) True b) False

Q: Question 4 Find the derivative(f (x)) of f(x) =cos/x -/sinx a. -sin/x Cox " (x) = 2/x 2/sinx CSX…

A: By using derivative formula

Q: Question 11 puas √1+1² Ffxx)=f -dt, then f'(x) equals 0 I+e' In(secx)√1+tan²x Itela tanx sec³x 1+ele…

A: Topic:- application of integration  Note :- as per our guideline if more than one question uploaded…

Q: 2. True or False. The dx [Arctan(tan x)] = 1 for all x in the domain. ans. True

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Q: O Question 9 Find f'(a) if f(x) = arctan(In z). 1 z (1+x²) 1 a sec²(In 2) 1 1+ (In 2)² 1+ 1 ()* 1…

A: To find the derivative of given function.

Q: Question 5 (i) Differentiate f(x) = sin Vx by the first principle

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Q: Question:2 Find domain of following functions S(x, y) = In(e*+e") arctan(x+y) а. f(x, y) = b. ( x² –…

A: The function in a will not be defined when x+y=0.  Thus, domain is:

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: Find the extrema of f(x) = 2 sin x − cos 2x on the interval [0, 2 ].

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Q: 6. (a) f(x) = arctan (e-2) 6. (b) f(x) = [arcsin (²)]³

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Q: If f(x) is odd and ∫-1 to 5 f(x)dx=11 then, ∫1 to 5 f(x)dx=?

A: It is given that f(x) is odd and

Q: (a) Sketch the graph of f(t) = sin 2(t- π)U(t - π).

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: -7-65-4 -3 -2 -1 -1 -2 -3 -4 -5 { -2 if x E | f(z) = { 4 ifx E Basic Interval %3D ( 3 ifx e DNE…

A: topic - functions

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = 2 sin x…

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Q: If f(x) = cos a- 5 tanx, then %3D f'(x) = %3D f'(5) =

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Q: sin t 元 If F(x)= [ dt, then F" 1S 1+cos t

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Q: 3) If f is continuous everywhere and | f(x) dx = 6, find sec" 2x · f(tan 2x) dx.

A: d/dx(tanx)=sec^2x Tan (pi/4)=1

Q: Find the limit of the trigonometric function.

A: The given expression is limx→06-6cosx3

Q: 10 - f sin(82) arctan(sin 4x) da integralinin değeri aşağıdakilerden hangisidir? a) O T-2 b) - 8 8(T…

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Q: tan ax x→0 sin bx f) lim ; a±0, b± 0

A: Given limit is : limx→0tanaxsinbx To find the value of the given limit.

Q: 2) Proof that If y = f(x) = = cos x then dx sin x

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Q: ,x € (0, 2] ,a = 0 f(x) = sinx then f (x) dx = 1 3 2.

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Q: Question 33 1 Point Let f and g be continuous on the closed interval [0, 5]. Suppose that / f(x)dx =…

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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: 133. a. Show that So f(x)dx = fo f(a – x)dx. b. Use part (a) to evaluate a/2 sin x -dx. sin x + cos…

A: ∫0a f(x) dx = ∫0a f(a-x) dx ∫0π/2 sin xsin x + cos x dx

Q: Question 1 Specify and sketch the domain D(f) of the following function sin(x + y) Va2 – y² + 1 f(x,…

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Q: Find f. f"(0) = sin(0) + cos(8), f(0) = 5, f'(0) = 2

A: Given, f"(θ)=sinθ+cosθ f(0)=5 and f'(0)=2

Q: 4) If F(x)= } d, then F'(x)- sin t

A: Note : According To our guidelines we can solve only first question and rest can be reposted.Thank…

Q: -sin x 0 [cos x - If f (x) = | sin x - 0, show that f(a)f (b) = f (a + b). 1] cos X %3D 0. 0.

A: Given: Here, f(a)=cosa-sina0sinacosa0001, f(b)=cos b-sin b0 sin bcos b0 001. Now,…

Q: cs x 5. If f(x) = | sin x - sin x 0] 0, show that f(a)f(b) = f (a + b). Cos x

A: To show thatf(a) f(b) =f(a+b)

Q: 4* What is the amplitude of f(x) 1 cos(TZ – 1) + 2? %3D 3 a. 2

A: Here we have to find the amplitude of f(x)=12cosπx-1+2

Q: 1. Find the most general f(r, y) obeying öróy - sin(x)y.

A: As per guideline we can solve only one question you can repost other questions in next question

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: Find f. f(0) = f"(0) = sin(0) + cos(8), cos(8), f(0) = 1, f '(0) = 3

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Q: 5. Find the extrema and the coordinates of the points of inflection for the graph of f (x) = sin?x –…

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Q: dx = In[F(x)]+C. what is F(/3) if C = 0? For (x+x³) (x Tan-'x + 1)

A: We will integrate the function first.

Q: 57. Extension of Example 8 Show that cos (x) is dx sin (x). 180

A: The objective is to show that ddxcosx° is -π180sinx°. The function cosx° is given in degrees bu the…

Q: QUESTION 4 Which f (z) is not analytic at 0 ? 1 o f(z) = z - 3 f(2) = !

A: Given that: f(z) is not analytic at zero.

Q: 4 sin x If f(x) = then 1 + cos x f'(x) = %3D f'(2) =

A: We need to find derivative of f(x).

Q: 116. a. Show that if ƒ is odd on [-a, a], then f(x) dx = 0. -a b. Test the result in part (a) with…

A: a.  Now put

Q: 5. (a) Find all functions y = f(x) satisfying dy/dx = sin(2x) + x. (b) Find the one function from…

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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: 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: The function f(x) = sin(kx) contains the point A(, -1). The function is: Oa) f(x) = sin(-x) Ob)…

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Q: If f (x) = - cos(x), then f (0)(x) is equal to A - sin(x) B - cos(x) В © sin(x) D cos(x)

A: We have to differentiate the given function 9 times

Q: 4 sin x If f(x) then 1 + cos x f'(x) = %3D f'(2) =

A: f(x)=4 sin x1+cos x We need to find f'(x) and f'(2)

Q: dx = In[F(x)]+C.What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1)

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Q: sin(1) Suppose F(x) = dt. Use the Fundamental of Theorem of Calculus to calculate dx (F(x). 9+1 (F<)…

A: To solve the following problem

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: 133. a. Show that b. Use part (a) to evaluate f(x)dx = Jo f(a – x)dx. •7/2 sin x -dx. sin x + cos x

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Q: Is there a value of c that will make sin² 3x f(x) = C, x = 0 continuous at x = 0? Give reasons for…

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