2-x Q.1 1 Write the function f (x) = =cosx+3x² as the sum of an even and odd functions.

Q: 8 +10x-32+x? cos 2x 4 Find : (a) y = %3D x2

A: Given y we have to find dy/dx as shown below

Q: 1. f(x) = 2x2 – 3x+4 2. f(x) = e-2x sin 5x %3D

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Q: Find a function of the form y = A sin(kæ) + C or y A cos(kx) + C whose graph matches this one: 6- of…

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Q: 1//2 x8 Evaluate: sin" (1-2x')+ cos" (2axvi-x")} dx. 2x²)+cos* 1-x4 -1/V2

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Q: A 61. f(x) = -2 cos (3x); 0 sxs 1/3

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Q: Evaluate D(sinx – 4e2) D³(sinx cos x-32 e В -cos x-32e2 C) -sin x-32 e2x (D sin x-32 ex A

A: The objective is to evaluate, D3sinx-4e2x

Q: Find a function of the form y A sin(kx) + C or y = Acos(kx) + C whose graph matches this one: 13 -12…

A: We can note that graph is having maximum at t=0. So graph must be cosine. lets see the graph of y…

Q: Choose the correct graph of F(x) = 2 sin(2x + T): 2 1 27. 3 -1 -2

A: Find your answer below

Q: 1. Determine if the function is even or odd g(x) = f(t) = sin 21 x2-9

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

Q: 2) x- 2y = x°cos4x

A: Given differential equation is -   xdydx-2y=x3 cos 4xDivide throughout by x we get-dydx-2xy=x2 cos…

Q: Choose the correct graph of F(x) = 2 sin (2x+ t): 1 27 37 -1 -2

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Q: b. f(x) = -3 cos [4 (x -+ 2

A: Givenf(x)=-3cos[4(x-π8)]+2.

Q: Q1-A/Find the domain of the following functions. 1-f(x) = √(sin(x) - 1) 2-f(x)=-/In(5x-x²/4)

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Q: IT 5. h(x)=cos x+ 2 n(x) -(х-3)* +4 6. 7. W (x)=e**2 –3 x+2 8. f(y)=(y-1) +2

A: We draw garph of following function

Q: 1 (27 x sin nxdx 27 bE f(x)sin nxdx -sin nx -1. 1-2n cos 2nn COs nx %3D %3D The requirod f 2)

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Q: Evaluate D³(sinx - 4e²x) A -sin x-32e²x B -cos x-32e²x (C) с cos x-32e²x D sin x-32e²x

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Q: Evaluate D3(sinx – 4e) A cos x-32 ex B -cos x-32 e?x -sin x-32 ex sin x-32 e2x

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Q: we can write the given function as: x(t) = 3 + 4 cos (20nt + ) 2 sin (60nt -)-4 cos (70nt – π) As we…

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Q: -x² 9 d. f (x) = xe [0, 5]. e. f(x) = |x² − 4], [0,3]. sin x f. f(x) = = [-ㅠ -π, π]. x² + 1

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Choose the correct graph of F(x) = 2 sin x; - < x< 2 T: Av 2 1 -1 -2

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Q: 7. Find and sketch the domain of the function f(x, y) = 2 ln(49 – x² – y²) + 8/ -

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Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

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Q: The action of a waterwheel can be modeled by the function y = 3 cos(T (x - 3) + 2). Within the…

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Q: 5(t - )cos3t) 3 252 + 18

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Q: Suppose f"(x) = -9 sin(3x) and f'(0) = 2, and f(0) = -1. f(T/3)

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Q: |Suppose f"(x) = -25 sin(5x) and f'(0) = 2, and f(0) = 1. %3| f(t/3) =

A: We find f'(x) by integrating then find C using f'(0)=2

Q: 12. Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 3 2x 11-8 n x³ + 1/ 5 where [ ] = G.I.F If lim /2n dx = k, find the value of [1] + 2013.,

A: Solution :

Q: - 6 3 y =x sin x + x cos 2

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Q: -1 -1 18. Show that cos (-x) =T- cos x

A: We have to prove that cos-1(-x) = π - cos-1x

Q: 55. f(x) = x² + cos ¹x on [-1, 1]

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Q: 1. Find the domains of the following functions. x2 - 2x 2.x-3 (a). f(x) = (b). f(x) = (c). f(x) = 3…

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Q: 2 The difference between the greatest and least values of the function is 2 2 - f(x) = sin 2x- x on…

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Q: 12. If f(x)=sin(2x+1), then f'(x) is equal to A -2 cos (2x+1). 2 cos(2.x+1). 4 cos(2x+1). C D -4 cos…

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Q: 4. f(x) = sin xand g(x) = 2x 5. f(x) = x² + cosx and g(x) = 3x + 4 Guide Questions: 1. How did you…

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Q: -1 -2<x< - 1 0 -1<x<1 1<x<2 nswer: f(x) = a + Tin COS ... COS n=1 sin T²n² O sin () COS

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Q: Sketch a graph of the function f(x) = sin(x). -7/4 1/4 1/2 3n/4 57/4 37/2 77/4

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Q: Evaluate D³(sinx - 4e²x) (A) sin x-32e²x (B) -cos x-32e²x C -sin x-32e²x D cos x-32e²x

A: Finding the third derivative of the function

Q: - 7x +2 g (x) = (x + 1) (x – 5) h(x) = -2 cos x+5 y = 4(x + 1)³ –7 x2 y = 4*+2 f (x) = -3x° + 6x¬² –…

A: To organize the following equations a polynomial or non polynomial.y=15x4-7x+2gx=x+1x-5y=5x2hx=-2…

Q: The domain of the function * sin x f –(x) = g x2 – x + 6 -

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Q: Graph the function. f(x) = -3 + cos(x)

A: As we know that if fx transform to fx-a, it means that graph shifts vertically downward by a units.…

Q: k. [₂ x cos³ 2x sin 2x dx

A: According to the company rule we can answer only first question and rest can be reposted.

Q: 2 Sketch a graph of the function f(x) = 2 sin (-) 6+ 4 2 -8 -7T -6A -5T -4T -ŽA -2T 2π 3π 4π5π6ππ.…

A: To graph y=2sin(2x/3)

Q: Q3) Draw the following functions: (2-2x, x 3 1)f(x) = 2)y = -sin 3

A: Given: The functions are given as 1) f(x)=2-2x,x&lt;-14, 2x-2-1≤x≤0x&gt;3 2) y=-sinπx3   To graph:…

Q: 5. Draw the graph of the function: f (x) = -4Cos (x -) + 9 over the interval 0<x< 2n. 6. A. ra w ert…

A: 5. Given function is and the interval is Graphing the function using a graphing utility:

Q: Choose the correct graph of F(x) = 2 sin(2x + T): 2 1 十4 -1 -2

A: Given query is to find the graph for the sine function.

Q: Evaluate D6(cosx+e-2*) (A sin x +64e -2 B cos x – 32e-2r (c - sin x – 32e-2x cos x + 64e -2x |

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Q: (1) f(x) = {"x, r0, if - 2<x<0 х, if 0<xs2 O F«) = { 0, - n<x<0 0 <x<n sin x,

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.