15. Sketch the function g(x) = -3 cos 2 (x -) +1 on the grid below: [4] y ok Air

Q: Consider the function h (t) = e-3t cos (2t) . Compute h' (7/3) - Number FORMATTING: Give the value…

A: In the given question, concept of derivative is applied. Derivative The derivative expresses the…

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

A:

Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

A:

Q: The function yow) satisfies the differantial equation x dy + ay Cos(xx) ak y(1) = 1 , the valu of…

A: Given differential equation is  xdydx+2y=cos(πx)x,y(1)=1

Q: Suppose z is a function of x and y. Solve for ∂z/∂y if tan √(y^2 + x^2 + z) = z^(x)e^(6y).

A:

Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

Q: 3 Use the definition 平grien FuncTionsEat'co,): for ー X+y X-ツ ix=ツ ) fory) =) singty4) ーty2 (x) #…

A:

Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

Q: lue of c is the following function co: CO In (cxy+1) if (x, y) + (0,0) 4) = ху

A:

Q: Consider the equation below. f(x) = 2 sin x + 2 cos x 0 ≤ x ≤ 2? Find the local minimum and maximum…

A: Given,          fx=2sinx+2cosx ; 0≤x≤2π

Q: Compute and * for the equation sin(x)e +2z²y = cos(z). 4xz COS ду

A: sinxe4xz + 2z2y = cosz∂z∂x = ?∂z∂y = ?   While calculating ∂z∂x  variable y will be considered as…

Q: 8. Sketch the following graphs for 0 < 0 <2n a) y= 3 sin x - 1 b) 4 sin 3x - 2

A: Topic = Graph

Q: 2. If f"(x) = 4 sin x +16 cos x, f(0) = 6, f'(0) = 1, find f(x) and f ().

A:

Q: Find y' for the following 1- y5 + x²y3 + 18 = ye*² 2- Sin(x + y) = y² Cos x 3- 3x²-2y³-1=0, find at…

A:

Q: f arctan y dy 3 ¥

A: Given problem:- ∫arctan(y)/y3 dy

Q: 1 For cos2(xy) = , evaluate y' when x = 1.

A: The given equation is cos2xy=14. Calculate the first differentiation y' of the given equation at…

Q: Let z be defined implicitly as a function of r and y by the equation əz 4+ In (ry²) - cos (xy - z) =…

A:

Q: Analyze the approximate value and the exact value for (7.2, 4.02) for the function z = x³y2 sin(xy)…

A: Below given clear explanation .Have a look in hand written solution below

Q: What is the average of f(x)=2 cos (x) + 2 e between x=-3 and x=2 12- 10- -3 -1 00 8 6 2- 0 T 1 X 2

A: Q

Q: 4.4. Show that the function f(x) = Sx² cos 1, if x = 0, ૨૦. if x = 0 is a BV-function over the…

A:

Q: Suppose that a y" + axy' + by = 0 has the general solution of the following form: y = x'(C1 cos (3…

A:

Q: 3e'x In cos2x Vxy = 1 y? x+1 7 In (xy)-3sin 2y |- 2y = 0

A:

Q: 29. How many periods are between o and 2n for the function y= cos5x. A. O B. 3 C. 2 D. 1 E. Not…

A: We have to find  no of period

Q: Calculate L4 for f(x) = 24 cos () over %3D LA

A:

Q: 9. Find f(35) (x) for f(x) = cos (2x)T = COS

A:

Q: x = Cịcos (At) + C2 sin (At)

A:

Q: Show that where n is a positive integer.

A: To show

Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – z) =…

A:

Q: ii. Verify that the u = -e-Y tany is harmonic in an appropriate domain D.

A: Given that u=-e-ytany.  If u is harmonic then uxx+uyy=0.

Q: Find a function f that satisfies the equation | f(t) dt = 2 cos x + 3x – 2. %3D -

A: Derivative of a definite integral is: ddx∫0xf(t)dt=f(x) Formulae used: ddxcosx=-sinxddxx=1ddxC=0…

Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: 1-Let :=x+iy then cosh(iz ) is equal to a-cos' y+ sinh' x b-cosh' y-sin'x e- sin' x+ sinh v d- None…

A: Let z=x+iy therefore, iz=ix+i2y=ix-y=-y+ix we know that  coshz=ez+e-z2 therefore, cosh…

Q: 7. Differentiate the following functions. sec (x³+1) b. у 3 cos yx

A:

Q: EX/ If f (x)= + COS2X CoS X is Pcx) Continlacaus at x=? %3D

A:

Q: 13 20 Find for Two only of the following: dx 1- y=xtanhx 2- y =cosh 3x- sinh²3x

A: We have to find derivative

Q: 1. Consider the two functions f (x) = cos 4x and g (x) = ) (a) Write down: (i) the minimum value of…

A: Given: fx=cos4x, gx=x2 we know that cos4x∈-1,1∀x∈R so, minimum value of fx is -1 now, we know that…

Q: Q4. Given that: z = y sin(2x) + (1+x²)e* + cos x tan-1(y* + 1) In(y6 + 137)

A: Given that, z=y sin2x+1+x2ex+cosx tan-1y4+1 lny6+137 ∂z/∂x is the partial derivative of z with…

Q: - Show that the following functions satisfies the heat oquation = . (e>0, constant). 1)2 =e sin .…

A: Since you have posted multiple questions, but according to guidelines we will solve first question…

Q: Given +2 – 25 dt 1+ cos2(t) f(x) : At what value of x does the local max of f(x) occur? Preview

A: Consider the given function.

Q: If it was f(x,y)=y cos(6xy) SO a² f Əy² 2² f Əy² a² f Əy² a² f Əy² = 36 x²y cos(6xy) + 12x sin(6xy)…

A: A detailed solution is given below.

Q: 1%1… l.令 > OX 101:00 i learn.ejust.org/current, :D tan-(x) dx = %3D V3 n - In (8) - In (2) V3 None…

A: Since you have asked multiple question, As per our guidelines, we will only solve first question.…

Q: Consider the function f(x) = cos x − 3x + 1. Since f (0)ƒ () <0, f(x) has a root in [o,]. If we use…

A:

Q: 1. Determine the relative extrema of the function y = 2 cos x + sin 2x on the interval (0, 2Tt). %3D

A: To find the extrema of the function

Q: 2. Consider finding the root of f(x) = e"(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

A:

Q: dy.xandy in =cos = COS e

A:

Q: 1 find the value of so that ky"=-1 at y= For cos x- sin y=- O V3 2 4 4

A: Solution:-

Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…

Q: Suppose x and y are functions of a third variable t If sin2(x) + cos²(y) =- and dr dy what is the…

A: