1. Obtain 10 samples of x(t) = 2 cos (10t) from t = -0.3s at a sampling frequency 10Hz. Plot a.) x[n] b.) x[n +3] c.) x[n - 5] and find X(z).

Q: 1) Solve the ODE below. a) x²y" - 3xy' = x²

A: According to Bartleby guidelines I have solved first, since this is not interrelated question,   For…

Q: Q2) 1- Find for: y= cos (x)+cos(x*) CoS

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Q: Given α+ßi = √¹x³¹_x=¹¹dx, Inx 0 α, ß ER, find the analytic expressions for a and

A: Recall the following formula  ln(a+bi)= ln √(a²+b²) + i tan-1(b/a) .

Q: 4. Find y if ((2x+7)dx x +4x+8 I = -1 tan y + C In|x² + 4x + 8 + 1⁄2 ta

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Q: Let e4 – sin(x + y²) – VTY. Match the following. A. 4e - cos(x + y*) - | - 2 ay B.-2 cos(x + y²) +…

A: Given,f(x,y)=e4x-sin(x+y2)-xyDifferntiating both the sides w.r.t. x…

Q: Find the domain of y = cos ¹(2x).

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Q: a. +4 cos x +6 sec x – 5 ) dx 2 x5

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Q: sin(2t +) dt = 64 7.

A: Note the formula for the integration by parts : ∫utvtdt=ut∫vtdt-∫dudt∫vtdt .

Q: Ln denotes the nth Lucas number. (L1 = 1 and L2 = 3 and Ln = Ln-2 + Ln-1). %3D Find the 6th Lucas…

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Q: Show that Loo (1 COS X (1+x²)² dx кіо π e

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Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: (1.1) Calculate the following: (2² + y? – 3xy + sin(x²y+ y?)). -

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Q: 7. Prove that d dx [cos ¹ x] = = 1 √1-x² x2

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Q: 7) Suppose cos(x – y) = xy. Find at the following points 7.1) (0, 5) 7.2) (0,– 5)

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Q: a) Find for 5x² – x³ sin y + 5e*y = 10 dx

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Q: [*(sin³r)√1 + cos ar dr x

A: We know that integration power rule is given as  Integration of xn is xn+1/n+1.   Here i attached…

Q: If g(x) = Cos x – Sin x a) Find g() and g (#) 8 b) Show that g ( - + x) = g(n – x) .2

A: sin(π2+x)=cosx cos(π2+x)=-sinx sin(π-x)=sinx cos(π-x)=-cosx

Q: Ln denotes the nth Lucas number. (L₁ = 1 and L₂ = 3 and Ln = Ln-2 + Ln-1). Find the 5th Lucas…

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Q: Evaluate. | (sin (r))* (cos (x))“ dr

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Q: 11.1.5 Show that (a) cosx = Jo(x) +2(-1)" J2n (x), n=1 (b) sinx =2)(-1)" J2n+1(x). n=0

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Q: 2. Find cos ec (In x) dx . x1+ cot(h x)

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Q: H.W Use N.R.S method to solve the f(x) = tan x - x, using x0= 5, and use three iterations.

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Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: . Evaluate f dx using trigonometric substitution. x/4+x2

A: Given integral is ∫1x4+x2dx. We have to evaluate ∫1x4+x2dx by using trigonometric substitution.…

Q: Find the average power of the signal: x(t) : = cos x + sin x (-7/4, 0) (7n/4, 0)

A: From the given graph, it is observed that the period of function is T0=7π4--π4=2π. Compute the…

Q: Π . For 0 < x <- , if y = (sin x)*, then find 2 dy dx

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Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: b) S x² cos(2 x³)dx

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