) Sind dy if : Sincu, u= x

Q: If sinr = In y, show that dyOUTM dr OUTMO (1--- (1– 2) dy = y. dr

A:

Q: HiW Ys Sin u , ノ

A: Explanation of the solution is given below...

Q: Find : dw/dk α w=2 sin m ka 2

A: To find dw/dk for the given w

Q: dy If y = sin='(cos x) then dx ||

A:

Q: az -? Since it is du coSV.y=. av ) z = In (xry*),x = e"cosv.y= e"sinvr

A:

Q: Show that sin a – sin b < Ja – b), for all a and b. (Hint: MVT) use -

A: Mean Value Theorem :  The mean value theorem states that a function f which is continuous on the…

Q: Ex 15: Prove that : d du tanh u = sech2 u dx dx Proof:

A:

Q: show that Itu X tvl = Oe sinu far a sphene of a radus a depined Panamet ui call y by 9 cU,V) =a…

A: Given: Parametric form of a sphere with radius a…

Q: Show that 0, if m if m + n sin(nx) sin(mx) dx T, = n IT

A:

Q: Find dy/dz in terms of e and y if arctan(x®y) = ry°. ||

A: See the details solution in below

Q: In AXYZ with a right angle at Y, the cosine ratio can be used to find the length of XZ as O a) XY…

A:

Q: dy is let y = (sin æ)*an 7 then dx

A: Given

Q: If y(u) J5 COs v9 dv then cos(9u eIu y'(u) = %3D e4

A:

Q: If z = cos (r + cos y), show that az Fz ar ərðy dy dr

A:

Q: find dy ny the Chaenin Rult yz tan u and UzJxz+5

A:

Q: dy if y=| cos Ode dx if y= [ cos Od0. Use the Fundamental Theorem to find 3

A: We will use newton leibniz theorem to answer the given question .

Q: Let y=9 In(cos(es). dy = AeBt sinC (et) cosº (e6t) Then where %3D В 3 B = C = = D =

A:

Q: dy If y = arctan(er), dx

A: NOTE: Refresh your page if you can't see any equations. . the given equation is  take derivative

Q: Suppose f(x, y) : where x = r cos 0 and y = r sin 0. 4 af af and ar Find when r 1, 0 -

A:

Q: cos @ t sin* O) de = sin O dr %3D

A: Given differential equation (2r cos(theta) sin (theta)) d(theta)=sin(theta)dr Now we will evaluate…

Q: Given show =5 how dy %3D

A: differentiate y with respect to x .

Q: If u = e3x. du = 2 cos 2x dx then du = 3e* dx, v = sin 2x. Select one: True O False

A: Differentiate the equation u=e3x with respect to x.…

Q: L[cosh(@ot) u(t)], C[sinh(@et) u(t)] and L[cos (@t) u(t)

A:

Q: as Let ĝ +sinh (z?) - ji = 27 where w=f (x,y,2)- %3D Find 2 nd JW and au

A: In the given question we have to find the partial derivatives of with respect to x ,y and z. here we…

Q: dz and du dz Find when u = In 2, v = 1, if z = 10 tan'x, and x= e" + In v. -

A: Here we the chain rule to get the answer .

Q: If y = sin(msinx) then show that (1– x)' y, – xy, + m² y =0.

A: Given: Given y=sinmsin-1x We want to show that 1-x2y2-xy1+m2y=0

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

A:

Q: By the samc way, prove that g 7 sinw.k MUIS Z N-27 cesW. +1

A:

Q: Find dy dx? A) y = 3sin u - sin'u and x 3 cos u- cos'u

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

Q: Te 2=tnx then prove thot dx 28 Snメー tty? 1+xて

A: We have to use proper calculus applications.

Q: Sinex dx is a) Conv. to o 6) diverge b) cont. to 프 auou (P

A:

Q: Evaluate. S cos a In(secz)dr COS D

A:

Q: az Find when u = 0 and v dv 117 if z(x, y) = sin x + cos y, x = u •v, and y =u + v.

A:

Q: dy If tan y = X, then dis %3D

A:

Q: Evaluate [y cos (3y) dy

A: We use integration by parts continuously. ∫f(y)g(y)dy =f(y)∫g(y)dy  - ∫df(y)dy(∫g(y)dy )dy Also note…

Q: Sind d Cor Tue fundion y. Sin (Incax)olncsin' cas)

A:

Q: a) Find dz, if z = e' sin e %3D b) Verify uxy = uyx , if u = In /x² + y² . %3D

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

Q: 20, Yu,t e Rt ond Yc eR Dimension (R) = ? %3D

A: This question is related to linear algebra topic dimension of vector space.

Q: Let 3 sin x + 7 cos y = 3. dy %3D dx d²y dx?

A:

Q: Find ſ z2 sin z dz

A: We can find the integral in the following steps

Q: EXpress ume trig fatIOS as TTACCTIOTIS TII Smmpiest teTIIS. 16 R. V33 17 sin R = Cos S sin R and cos…

A:

Q: -41 sin tZ dz, c: 1Z-il=2 z4 ans: 3. coshz dz ,C: IZ1=1 27T ans :

A:

Q: Show that w°sin(xw) пе dw= 2 cosx if x > 0. w* + 4

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Q: dy Find if y = In|9 + x|. dx

A:

Q: If z = exy where x = In(u + v) and y = sin(u-v), find az and az du

A: We use the partial derivatives and chain rule of differentiation to answer the given question.

Q: If x=sin8,y=0 ,y=cosp0,Prove that (1-x') y,-xy,+p°y=0 where y2 d'y dy and y,- dx? dx

A:

Q: dy _ 2y 4. If tan(ry) + 5= ry then show that dr?

A: We have to do differentiate with respect to x.

Q: dy 1+ sin 4y

A:

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…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.