QUESTION 1 d²y Find dx² for each of the following equations. a) y = 3x² + cos(3x) b) y = e** + (x + 1)+

Q: Зх — бу — 2z %3D 1 2х — 4у + z %3D 17

A: We can use an augmented matrix to solve the given non-homogeneous system of equations.

Q: de 2 C:and 0.1784 arctan + C; and 0.1784 arctan aretan k- + C; and 0.1784 arctan

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Q: Find dw/dr and dw/dΘ for w=2z/y-3x if x=3Θ+2r, y=3r^2 + Θ, and z =4r-Θ, where Θ = 2 and r = 5.

A:  w=2zy-3xx=3θ+2r,y=3r2+θ, z =4r-θTo find ∂w∂r and ∂w∂θ for θ=2 and r=5

Q: Find f'(x) for the function. x) = 7×(17%* 15 f(x) = 7x(17. x + 1 105x 595x + f'(x) = (x +1)2 *

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Q: CAn equation of the plane through the point (2, 5, 7) that is parallel to the line 7 (t) = 3î + 2ĵ -...

A: Given problem:-  Find an equation of the plane through the point (2, 5, 7) that is parallel to the l...

Q: How do you do this in properties of addition.

A: Our Aim is to apply the properies and to solve the fractions given below:-(2) 39+59+49(4) 426+246+33...

Q: csc xcot x sin(csc x )dx

A: ∫cscx cotx sin(cscx) dx

Q: 2n5-n2+4 i. an n²+1

A: Follow the procedure given below.

Q: л- 25х — х? — ху - 2у? + 30у - 28

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Q: 2) Explain in your own words what is meant by lim f(x) = 5. x→2 Is it possible for this statement to...

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Q: . Use the appropriate limit laws and theorems to determine the limit of the sequence. an=(3+8/n^4)^1...

A: We will evaluate all above as shown below

Q: Find the integral. e4X cos 3x dx + C

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Q: dt 15+2t-t

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Q: Homogeneous Differential Equations (11) (x – y)dx + xdy = 0 (12) (x sin- y cos) dx + x cos 2 dy = 0 ...

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Q: e*dx e2x +1

A: We know that; ∫axdx=axlna+C And ddxcot-1x=-11+x2   Given: I=∫7cot-1exexdxe2x+1   ....1

Q: QUESTION 2 Differentiate of the following function with respect to x. a) y = x³ln (2x) 3x2+10 b) y =...

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Q: Find the solution of the differential equation ху V - ) (x+ y² + 1)dx - (y dy = 0 %3D Vy2+1,

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Q: Find two positive numbers with product 361 and whose sum is a minimum. Enter your answers in increas...

A: To find, two positive numbers.

Q: Linear Differential Equations (20) 3xy' – y = In(x + 1)

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Q: Evaluate the given function ſ sec5xtanxdx a. sec*x + C b. sin*x + C c. cosx + C d. 금esc5x + C

A: topic - indefinite integral

Q: the given position vectors r(t) compute the unit tangent vector T(t) for the given value of t . A) ...

A:

Q: A' + BT

A: Given: A=11134-6424848-56526117B=3-4858122646742638 To Find: A-1+BT

Q: The average change of a function f over an interval [æ1, x2] is f(m2)-f(#1) First find the average r...

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Q: Evaluate the given function ſ tanøsec?ødø

A: Hence, the correct answer is option (d)

Q: tan? 0 8. -1= tan 0 sin? 0

A:

Q: 3. Find the 8th term in the binomial expansion of (x² + y³)10. correct combination, evaluating combi...

A: We will find the 8th term. 

Q: 2. Let f(x) ax+b cx+d° %3D (a) Show that if ƒ is one-to-one, then ad – bc # 0. (Ъ) Show that if ad –...

A: Given that: f(x)=ax+bcx+d

Q: Vrite out the first five terms of the sequence with, In(n) n+1 determine whether the n=1 sequence co...

A: We will find the limit 

Q: (4x^4+x^3(y)+y^4)dx+x^4dy=0, Solve for HOMOGENOUS DE

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Q: Determine the particular solution of y"– 3y'+2y= 4e"; y(0)=-3,y'(0)= 5 using Laplace and Inverse Lap...

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Q: iv. An = In(n + In n

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Q: do not evaluate)  When finding the volume generated by revolving y = 2 − x^2 and y = x^2. JUST Set ...

A: Given: y=2-x2y=x2

Q: Consider lim e-. a) lim 4x - x² = 0 b) If we let t = 4x - , then we can rewrite the limit as lim of

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Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

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Q: Consider the surface given by the equation z - y = x2. Draw a total of at least 3 traces in at least...

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Q: 1. A thermometer reading 180C is brought into a room where the temperature is 700C ; 1 minute la the...

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Q: Proof 2: 14 sin x dx tan xdx = /6 COs x 1 -= sec x dv = sin xdx cos x du = sec x tan xdx v =-cos x 1...

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Q: 3- 2-6 -3 -2 -1 1 2 3 The following function is discontinuous at three values of x. List these value...

A: We will find the point of discontinuity. 

Q: 1 Find the vertical and horizontal asymptotes of the function f (x) = , where q (x) = (ya+10)(10 – x...

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Q: A. Find the differential equation: (1) whose general solution is y = c,e-2x + cze3x (2) by eliminati...

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Q: find the equation of y where dy/dx = 3x + 5 and y= 6 when x = 0

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Q: xl² -1), 2 x +1

A: To evaluate:∫xx2-1x2+1dx

Q: 3. Find the 8th term in the binomial expansion of (x² + y³)10. correct combination, evaluating combi...

A: The nth term of the binomial expansion of (a+b)n is given by: Tr+1=Crnan-rbr...(1) Here, to find the...

Q: Determine the solution to the initial value differential equation y' = 0.0012 y (2900 – y) , y(0) = ...

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Q: Find the general solution of У" - Зу + 2у 3 2х3 - 9х? + 6х

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Q: Given the differential equation d?y 12. + 4y = 0 di? Determine the Characteristic Equation for the g...

A: We have to find characteristics equation

Q: Find the sum of the infinite series, if it exists. -16 -64 32 8, , 5, 27· 3 Enter the sum as a fract...

A: The given infinite series,8, -163, 329, -6427,.......

Q: Use the comparison theorem to determine whether the integral is convergent or divergent. dx 3 + x12 ...

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Q: 12. Use the factor Hheveto determine whether x-C Isa fultol. offd.

A: (11). The given function is: f(x)=x4+8x3+12x2 ;       x+1

Q: 7. Find the x cand y nvercapts of f fG)=4hx" (x+7)3

A: Topic:- algebra  Note:- as per our guideline if more than one question uploaded than only first ques...