et sin x — х - lim x → 0 5 cos x – 5 ||

Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

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Q: (10 pts) Evaluate the integral. (Hint= cos(x)+cos(x)tan % ² (x), sec (x)

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Q: If f(x)= cos (x)+3x , what is f'(x) ? COS O f'(x)=-sin (x) +3

A: First option is correct. Explanation is given below....

Q: 2 lim In (cos x)e

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Q: (a) f(x) = sin(x) X at x = 0.

A: a.the function is not defined at x=0. The function has right hand and left-hand limits same and…

Q: 4. sin 'xcos 2 O J sin xcos"xdx (8)

A: NOTE: You have posted multiple questions we have given answer to the first question if there is a…

Q: Find f'(÷) for f(x) = 2 sin z cos 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: If f( x ) = sin (x) – e“ , what is f'(x) ? O f'(x)=- cos(x)-e² — сos(2) —е* O f'(x)=sin (x) –e² O f…

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Q: If j(x) = e(sin(x)+cos(x))² , then j'(x) = 2 cos(2x)el+sin(2«) COS

A: Given

Q: nx and y=cosx from x=- to x=- 4 4

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Q: Find f(x) given that: f'(x) = 2 cos x -3 sin x and f (주) %3D %3D

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Q: (In x |cos(In x) dx X.

A: Find integration

Q: coS x dx 6) 1 + 3 sin x A) In| 1+3 sin x|+C C - 를 In| 1 +3 sin x| +C

A: To evaluate ∫cosx1+3sinxdx

Q: -sin (In x?)ecos² (In x) dx 100x2-x2e2 cos (In x)

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Q: d) f(x) – e) f(x) = sin [In (x² - 3x)] sin x f(x) = 1+COS X

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Q: dy Find as a function of x when y = sin°(x) %3D O 1) 5cos (x) 2) 5sin (x)cos(x) 3) 5sin (x) 4) 5cos…

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Q: If f(x) = COS X then f' (x) equals: X S0)- -sin x cos X:

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Q: The "equation cos x "y sin x is A Iny In (cos x) + k B Iny = In (sin x) + * c. Iny=-In(sin x) + k…

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Q: (d) lim In(cos r) エ→0

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Q: Find the absolute extrema on the interval [0,2π] for f (x)=x/2+cos x.

A: Absolute extrema

Q: (1) (sinz) + (cosr)* sin x COS x (2) tan x in terms of sin x, cos x %3D d. d. ( sin x COS X %3D dx…

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Q: Find F'(x), f"(x) and f'"(x) for f(x)=x$+cos(9x).

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Q: Q! O show th at [x sin'x + V1-x²] = sin'x sin x

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Q: Find the absolute extremum point(s) of f(x) = e1−cos x  on [−π/2, π), if any.

A: The given function is                                            f(x)=e1-cos x And we have to find…

Q: Prove that: cos(nx) - cos(na) cos(x) – cos(a) sin(na) sin(a) dx = n neN, a ER - {0}

A: To solve this question take different values of n and calculate LHS and RHS separately.     if…

Q: (1) y = In(x+ 4)- x tan (2) xy + xy x + 3y (3) Iny e' sin

A: In this question we will use basic of calculus i.e concept of differentiation. We will simply…

Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: Let f(x) = cx + In(cos(x)). For what value of c is f'(n/4) = 9?

A: f (x) = cx + ln ( cosx)To Find: For what values of c is f' (π4) = 9Proof: We will differentiate f(x)…

Q: If f (x) = - cos(x), then f (10) (x) is equal to (A) - sin (x) ® -cos(x) © sin(x) D cos(x)

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Q: on f(z) = e cos x+ ie-Y sin x is entire.

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Q: Evaluate in x cos x dx. .3 I COS" T

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Q: 1 Find the L s(s²+1) O 1-cos x O 1+sin x O 1-sin x O 1-cos x

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Q: /3 dx cos x tan x /4

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Q: If f x?cos x dx = f(x) – S 2xsinx dx, then f(x) is _ A. 2 sin x + 2x cos x + C B. x²sin x + C C. 2x…

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Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: tan(In x) 1. Evaluate: dx A. In cos(In x) + C c.tan?(In x) + C B. In sec(ln x) + C D. tan(In x)² + C

A: The given integral is ∫tan(ln x)xdx

Q: the integral of tan^2 (x) cos^3 (x)dx

A: To evaluate the given trigonometric integral

Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

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Q: Find F' if rsin ) = /" 4 nin" t t. F(x) = cos-lr

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Q: -8. sin f(x) dx where f (x) sin x if 0 <x < T/2 cos x if T/2 < x < T

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Q: 13. ebx cos x dx exists only when b < 0. lim t→∞

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Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: Find f'(x) and f'(c). Function Value of c COS X f(x) = ex C = 0 sin x + cos x f'(x) = et f'(c)

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Q: 3. If w-f(x.y) and x-r.cose, y-r.sin6 Prove that - A + fy ar

A: Given that w=f(x,y) and x=rcosθ,y=rsinθ Prove that ∂w∂r2+1r2∂w∂θ2=fx2+fy2

Q: 25. If f(x) = (cos x)*, then %3D is k-0

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Q: 2tan x In (cos x) dx= A sin x [In(cos x)] + c cos x [In(cos x)] + C © -[In(cos x)]? +C D [In(sinx)]?…

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Q: Find the absolute extrema of the function on the closed interval.                         g(x) = 2x…

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Q: If g(x) f'(x) and if g(x) (cos x - x sin x)e*cosx, then f g(x) tan(f(x))dx is x cosx In(e*cosx) +€…

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