find all values of unknowns which satisfy the following equations: 1. (x, y, z) - 3(-1, 2, I) = (0, 0, 0) 2. 7(2, x, x^2)-5(2 -x, x^2) = (1, 12x, x^2)+3(1, 0, 1) 3. (sin x, sin2x, lne) = (sinπ, 2sinx, secx) cosx

Q: Four equations are provided below. Which equation follows from the Power Rule? I. (P)' = pr P 1…

A: Answer is option (a)  Because only equation 3rd follows the power rule .

Q: What is the formula for integrating sin 40 cos 20d0 ? S (sin 60 – sin 20) do S (sin 60 + sin 20) de…

A: SOLUTION-

Q: y" – 9y = t° – t e + sin(3t)

A:

Q: Find y". y = 6 sin(2x + 10)

A: Given,            y=6sin2x+10

Q: Find dt 1- t2 sin (t)

A: Solve the integration

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: / (csc 2x)(cot 2x cos 2x + cot 2x cos 2x) dx

A:

Q: D?/if w= Cos (X+y)+Sin (X-y) Show that

A:

Q: 1. find the linear approximation tof (x) at x = xo. Use the linear approximation to estimate the…

A:

Q: How would this parametric function of x=2cost +cos2t; y=2sint-sin2t be solved

A: In order to solve a parametric equation, firstly differentiate x and y with respect to t and then…

Q: 6. sec (sin-1 x)

A: Interconversion

Q: 4 sec(8) = find cot(0) 2

A: Use trigonometric rations

Q: Q6/ Solve Sin() dx, Compute R4,4, then find error ratio

A:

Q: dy -y'sinx is: dx The solution of Select one: a. y3cosx+ C O b. %3D COSX-C C. V=3 CO5X + C d.…

A:

Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

Q: (- + 2 cos 2x ) dx + (- - 2 sin 2y ) dy = x2

A: You have asked multiple questions in a single request. As per our honor code, we will only solve the…

Q: 10x 19) y Sin'(5x') (ans.: JI-25 x' 20) y= Cot ) (ans.: 1+ x' 6x' 21) y=tan'V4x'- 2 (ans.: (4x'-1…

A: As per guidelines we can only solve first question or first three subparts of the question, I am…

Q: Solve the he o-3D+4)y(x) =x cos(2x) equation y,(x)=(6x+4)sin( *+4)sin(2)-cos(23) - y,(x) =(-6x-4)…

A:

Q: Show that if y = V1 + sin x then sin x

A: We can solve it by doing derivative and make the proof.

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…

A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

Q: 2 x´ + 8)(6y – 1) = 0 find the third derivative

A:

Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: C- Find f' of the following: 1) √2x³-2² + In ² 2) 3xe³r+1 3) sin ¹(³).

A:

Q: I. Functions and Limits 1) If f(x) = x2 – x + 3, find f(-5y) and f(x³) x2-1 2) lim X-1 2+3x-4 3) lim…

A:

Q: b) if J(zf64)} - 39ga) ) ce = Sin () %3D and S(3f (x)+9 6)) dx = tan () 2. 2. +596)) dx

A:

Q: Find (21) (22) if = 5 (cos 75° + i sin 75°) 22 = 5 (cos 35° + i sin 35°) Answer: Z1 = (2₁) (2₂) =…

A:

Q: instead of cube there is a square in that equation 3(2x-1)2 please solve

A: Given,           ∫2x-1cos32x-12+632x-12+6dx

Q: Find f, (x.y) and f, (x.y) Then, find f, (-4.- 3) and f,(-1,- 2). (x.y) = 2x°y? f(-4,-3)= (Simplify…

A:

Q: Solve the equation (y - (cos x)^2)dx + (cos x) dy = 0

A:

Q: What is the dependent variable in the equation dr + (2rcot0+ sin 20) d0 = 0?

A:

Q: 6メ-8) - $(4)= =1 Cos x (8-x9- 15) %3D

A: Since in part 1st given equation has no rational roots so I will do 2nd question

Q: Differentiate y with respect to a y cos²(a) + y sin²(a) = (cos(a)+37)² Select one: O a. y' =…

A: ycos2a+ysin2a=cosa+372

Q: Calculate facos xdx . (a) rsinr – casz+c (b) Icosz+sin x+c (c) zcost-sin x+c (d) Isinz+cOSI+C (e)…

A: Formula for integral by parts :        ∫u(x).v(x) dx=ux∫vxdx - u'x∫∫vxdxdx+…

Q: / (cos(x) + Ex dx 4 +

A:

Q: f'(3i) = -i, g(7+ 2i) = 3i, g'(7 +2i) = -4. Find (f o g)'(7+2i). 4i -4i 2.

A:

Q: 2) y = sin(3x²ex)

A: Find the derivative

Q: If A = A-¹ = 2e4t sin(2t) -2est cos(2t) -4e4t cos(2t) -4est sin(2t) 1/(2e^(4t) sin(2t)) then

A: