skatch f(H) ден httl ř (t) = trost i + tsint; ++k, -∞oct cos

Q: 1. Use any appropriate method in finding the indicated solution of the following differential…

A: (1).The given differential equation is:(1+lnx)dx+(1+lny)dy=0Now compare this differential equation…

Q: 3. g(t) = arcsin (E - find g'(t) A. (4-t+) В. (4-t+)ž C. - 2t5 (4-t4)ž 2t D. (4-t+)5

A: 3-Given- gt=arcsint22-t24-t4 To Find- The value of g't.

Q: S Q16) L−¹ {(8 − 1)² + 4) (A) et [cost + sin t] (D) et [cos 2t+sin 2t] (B) et [cos 2t + sin 2t] (E)…

A:

Q: Sketch a graph of x = -3 + cos(t), y =1+ sin(t), 0 < t < 27 COS 5+ 4-

A: Given: x=-3+cos(t)y=1+sin(t)

Q: 1 a²E(x,t) _ 0: a²E(x,t) əx² x E (-00, 00), t e [0, 0) c2 at2 ƏE(x,0) E(x,0) = sinx, = cosx at

A:

Q: Find y' where y = tan(11a? + 8) v173 + 17 Answer: 51a2 y/ = sec2 (22æ)\/172³ + 17+ tan(11a² + 8)…

A: I have used the rule for composition of function and multiplication of functions

Q: 6. (a) Recall that sin z = ¹2; cos z = (i) Find real and imaginary parts of sin z and cos z, for z =…

A: Note : '' As per guidelines we will solve first three subparts. If you want any specific subpart to…

Q: 2) f(t) = 4t3 sin %3D

A: we have to find Laplace transform

Q: 7. Set f(x) (a) (b) (c) (d) = 2 +4 8 cos 2x, 2sin2, + e-8/2 s² + 4 S s² +4 8 8² +4 (e) None of the…

A:

Q: 1. IF4=rzi-2y'?'j+xy's ,find ding at points (1.-1.1).

A:

Q: Prove that B(m, n) = B(m + 1, n) + B(m,n + 1)

A: given,

Q: E Let C₁ be the curve parameterized by r(t) = (cos² t, sint) where t = [-]. Let C₂ be the line…

A: Given that C1 is the curve parameterized by r(t)=(cos2⁡t,sin⁡t),t∈[−π2,π2].Let C2 be the line…

Q: Use the Chain Rule to find az/əs and âz/ât. z = x²y⁹, x = 5 cos(t), y = s sin(t дz əs əz at ||…

A: By using the chain rule to find ∂z∂s and ∂z∂t. z=x7y9, x=s cost, y=s sint

Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

A:

Q: (a) Define the symbols ôf/DE and af/dz by af 1 (af 10f 2 (dr af 1 (of 18f i by, dz 2 dr' i dy as…

A: Since you have asked multiple questions, we will solve the Question (a) for you. If you want any…

Q: For the relation siny – y² =x²y– x+x , is dx 3x²y+1 А. cos y – 2y –x T – 1 3x² + 2y – cos y cos y –…

A:

Q: y" = 2 Y y' = 5 + sin(y/x) 9x²y" = y + 3xy' 2xy²e(ry)² + 2x² ye(xy)² y' = 0 Choose... ✓ Choose...…

A: (.) Given differential equations are,(.)  First - order exact differential equation: A first order…

Q: (142) (2+) dx equals Q. 41 (z cos z + sin z)*

A: Solution of the problem as follows

Q: The values of C₁and C₂ so that y(x) = C₁ sin x + C₂ cos x satisfies the following conditions; y(0) =…

A: Here we have to find the value of c1 and c2 using given conditions.

Q: Q.13.a) s dx x2+2x+1 b) Sx sinvx dx dx c) J Tx+V% 1E / E

A:

Q: Evaluate tan" (x) sec4x dx. 1 1 A -tan 2) (x). + (m+2 -tan" (x) + C m+2 m (m+1) ¹) (x) (m- m+1 1…

A: Evaluate: I=∫tanmxsec4xdx

Q: 4) Graph y = arcsin x and z = arcsin (x-2) and w= arcsin (x/2) on the same axes Remember that these…

A:

Q: QU/A Find the domain and range for the following finctions: 1- y =Vx?-6 2- y = QI/B Prove that 1+…

A: Explanation of the answer is as follows

Q: z(r) = cos'(r)/1+r* ? cos (r) ( r Vi+r (1+r² 4 tan(r) cos'(-\/i + r*{ 4 cot(r) 1+r I tan(r) (1+r²

A: The given function is zr=cos4r1+r2.

Q: waluate Stan" (x) sec¹x de m 1 m+3 −tan (m+3)(x) + 1 m+2 1 m+1 1 m+1 1 m+1 tan n (m+2)(x) + — tan”…

A: We will evaluate the given integral as shown below

Q: 1. L{sc" sin wt} L{e* (acost+6 sin t)} -kt cosh 2t +-sinh 2t 2 3. L 2.

A:

Q: (b) Let n, m be positive integers. Define a function (2zm + 3)"e-3z sin?(z) h(z) = zm+2n cos3 (z)…

A: We will use definition of argument principle

Q: If f(x, y)= cos(x +y), then- (+: O a. - sin (x + y) O b. - cos(x+ y) COS O c. cos(x+ y) O d. sin (x…

A:

Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *() + 1. 2tan -1 2tan-1 + C ()…

A: