IER, t> 0, u(x,0) sin(87r) cos(90z). u + ru, =x

Q: Given that cos(x) = (-1x2 for e<xc than a powr saries of cas(x) %3D ie e (2n)!

A:

Q: Find dy/dx for the following : 1) y = x3 + sin x² + sin-1 5x 2) y = 32x + In (sin x²) + In(sin-1 5x)…

A:

Q: What is y' of y = sin¹ (cos x)? O A. y' = ATHE sin + 1-cos² 1 O B. y' = 1 OC. y'= sin z 1-cos² z OD.…

A:

Q: dy Find for y = tan-(3z) de Ans=

A: A detailed solution is given below.

Q: Determine the value of f(z) = e*cos y+ ie*sin y at z = In 4+ Ti/6

A:

Q: If x = t + 2 sin(at), y = 3t – cos(nt), evaluate at t =;

A: Given that x=t+2sinπt, y=3t-cosπt, we have to find dydx at t=12. Now, dydx=dydtdxdt…

Q: Determine the value of f(z)=e*cos y+ ie*sin y at z = In 4+ Ti/6.

A: For a complex number, z=x+iy , x is the real part and y is the imaginary part .

Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find f,(8,9,0). Leave your answer correct to two decimal…

A:

Q: dy -is: then dx cos. cos x Q21. If y = tan 1+sin x

A:

Q: 2. If z y where z= s cos t and y=s sin t, find az/ôs and az/at.

A:

Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: Differentiate y with respect to x where y= cos(-3x2)

A: Differentiate y with respect to x.

Q: The coefficient of sin(x) in the antiderivative of Flx)=(cos() is 15/32 (use fraction form not…

A:

Q: /hich of the following does not require the use of the dy nain rule to find ? dx A y = cos1 (10x –…

A:

Q: If z=In/x2+y2 +- tan 2 then the numerical value of + is equal to..... dy? dx

A:

Q: (t – sin t)v1 – cos t dt

A:

Q: dy iven that x = e" cos 3t, y=e" sin3t, show that tan 3t + dx %3D 4

A:

Q: Suppose that w = a7 · exp(2y) · cos(4z) with z- in (+ 5), x = sin (t+ y = In (t +2), z = t.

A:

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

A: z=ysin2x+1+x2ex+cosxtan-1y4+1lny6+137 Differentiating wrt x, we have…

Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: 0.6158 0.6165 None of…

A:

Q: Gren thint sin (A+i6) = xtiy, 28 Prove that, 9父+ =1 snh'B 1) x essec?A -y' sec'A =1

A:

Q: Given tanh(x)+ tanh ¯' (y) = 1, show that, 1- y? 1 – x² dy dx

A: Formula,ddxtanh-1x=11-x2Note- Since multiple questions are asked, I am answering the first question…

Q: dy let y = cos(In(cos(x))), then is dx

A:

Q: help!

A: Refer to the question, we need to sketch the provided function.

Q: Compute for the arcsinx dx . Which of the following is not an antiderivative of the function f(0) =…

A:

Q: @ / Find if dy O J= \ntanh (+2 の= Cos (Cosスー) O3=109,(e CSCX +Sinx)

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 220. Suppose f(x, y) = x + y, u = ex sin y, x = 1², and y = лt, where x = r cos and y = r sin 0.…

A:

Q: DIfferentiate the following fuh ction with respect to K In X %3D Sin a

A:

Q: d cosh z =sinh x dz صواب ihi

A: Use the formula of coshz and sinhz in terms of exponents.

Q: sin(iny)dy is equal to * y (A none of these cos(ny) + C y cos(Iny) + C (D) -cos(iny) + с cos((ny) +…

A:

Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: (1 + cos 9t) 2 sin 9t dt

A: ∫0π1+cos9t2 sin9t dt Consider, ∫1+cos9t2 sin9t dt Put, 1+cos9t=u⇒0-9sin9t=dudt⇒-9sin9t dt=du⇒sin9t…

Q: Let I = 3x*cos (x) dx. The approximation of / using the two- formula is:

A:

Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find fx(8,9,0). Leave your answer correct to two decimal…

A: Solution

Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. af and Or 1, 0 = 6 Find -when r

A:

Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) Oe2 0 0 O cos 2 O-sin 2

A: The given function is: fx,y=excosy   As we know that; The common derivative; ddxcosx=-sinx And…

Q: 3. Given that z= (u, v), where u 2r cos y and vz sin y. Find and Hence, show that Dy

A:

Q: O sin (z)cos(z)dz

A:

Q: A particle moves in the xy-plane so that its position at any time t is given by x= cos(5t) and y =…

A: According to the questionx=cos5ty=t3

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

A:

Q: Determine the concavity of y = 3 + sin x on [0, 2π]

A: The function y=3+sinx on the interval 0,2π. We have to determine the concavity of this function.

Q: Let f(x, y) = 2e sin(4) of д х of dy Check Answer

A:

Q: Given f(x,y) = e X cos y, Evaluate fx(0,2) cos 2 -sin 2

A:

Q: If y= tanu, u=v-- -, and v=ln x, dy at x= e? dx what is the value of

A:

Q: With the substitution u = sin(x), we get | 11 sin2(x) cos(x) dx = 11 u2 du. u? du. 11 %3D which…

A:

Q: y = C, sin at + C2 cos at, (a not to be eliminated)

A:

Q: I. Find dy/dx in the following: 1. Y= sin In(x + 1)

A: To find the derivative of given function.

Q: Given that: z = y sin(2x) + (1+x²)e* + cosx tan¬(y* + 1) In(y® + 137)

A: ∂z/∂x  is the partial differentiation of function z with respect to x, keeping other variables…

Q: dy is let y = cos(In(cos(x))), then da

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: If sin-r= In y, show that UTM dy (1-2) = y. dr

A: