Given pair of functions is (sin3x,4sin3x) O a. Linearly Independent O b. Linear O c. Nonlinear O d. Linearly Dependent

Q: find the value of the constants a, b S"L cos(x + 2y + 3z)dzdydx = TT a

A: Triple integral

Q: Find d2y/dx2 for the following functions: b) y = cos*(sec? 3x) 4 = COS

A: We are given : y=cos4(sec23x) ⇒dydx=4cos3(sec23x).(-sinsec23x).2sec(3x)sec 3x.tan…

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Q: 4. Find d?y/dx² for the following functions: b) y = cos*(sec² 3x)

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Q: Find a function 0f nH al =0 y Co) = 7 y (o) =/

A: The differential equation is given as y'''-8y''-y'+8y=0 The corresponding auxiliary equation is…

Q: Given f(x, y) = 3x* cos (y), find COS

A: Givenfx,y=3x4cosy5

Q: y to solve the following linear differe ] dy

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Q: dt cos?(t) V5 + tan(t)

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Q: find fx and fy of the given function        f(x,y) = x^y sin^-1(e^x+y)

A: Given: fx,y=xysin-1ex+y To find: fx and fy Solution: fx means patial derivative of given function…

Q: Separate the variables and evaluate the DE: cosx/dx + 1/ydy = 0

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Q: If (x) = tan(e"), then f"(x)= %3D A. 2e sec (e") B. 8e tan(e") C. 4e sec (e") D. 8e" sec (e*)tan(e")…

A: Given, f(x)=tane2x

Q: Which function is equivalent to f(t) = cos 4(t- T1/4)? *

A: Given that  f(t)=cos4(t-π\2)we need to find the equivalent equation from the given equation

Q: f(t) = cos(4t + 5) + e-tu(t – 6) + tcosh²4t |

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Q: Suppose z is a function of x and y. Solve for dz if tan Vy? + x2 + z = z"e6y.

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Q: Q2: Determine which of the following functions u are harmonic. (a) 3x?y + 2x2 - y3 - 2y? (b) 2xy +…

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Q: For the function y=4 sin (4x+Tt/2) +2 ... find a ,b & c

A: Given,  Wave function equation: y = 4 sin(4x+π/2) + 2 We need to find out the value of a, b and c…

Q: dz az and ду Suppose z is a function of x and y, and tan Vy? + x2 = ze6y. Solve for

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Q: Find f and f and evaluate each at the given point. Mx, V) = arctan(2). (6, -6) ,0x. y)= ,0 y) =…

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Q: Rewrite f(x) = 5 sin(3x) – 2cos (3x) in the form A sin (Bx + C). Round your final angle to two…

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Q: cos A where A = atjb

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Q: Which function is equivalent to f(t) = cos 4(t - TT/4)?

A: For two functions f:R→R and g:R→R to be equivalent, it means three things. First, the domains of the…

Q: B) If f (x, y) = tan (2x – 3y) find дх ду?

A: Given function is fx,y=tan2x-3y

Q: For the function y=4 sin (4x+Tt/2) +2 find a ,b & c ...

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Q: Is the function A cos (ka - wt = psi) a function of the operators ^ E and ^ T?

A: yes this is true

Q: Solve for the DE equation associated by the given function: а. у %3D Ае2х + Bе* + C.

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Q: Choose the value for a such that of 32 x² y cos(ax)dx d y = −4ñª 02 O None of the others O 2 0-2 O…

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Q: Which of the following pair of functions is linearly independent? (a) e, e(*-3) (b) 4, sin2x+ cos2x…

A: Which of the following pair of functions is linearly independent?

Q: Given 5y + cos(3y) = x³ Implicitly find dx Select one: 3x Sy²+sin 3y a. 3x O b. 5y²-sin 3y C.…

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Q: Evaluate the equation below rsin 0 r3 cos 0 dr d0 0.

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Q: Given x=sin5t and y=cos⁡5t, find the following derivatives as functions of t . a) dy/dx b)…

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Q: Find d?y/dx2 for the following functions: a) y = sin x2 cos 2x b) y = cos*(sec² 3x) c) y = x2(x³ –…

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Q: y = In tan(x – A) +B

A: Some Important Formulas 1. ddxtanx = sec2x2. ddxsin-1x = 11-x23. sec2x = tan2x +1

Q: Suppose the voltage in an electrical circuit varies with time according to the formula V(t) = 90…

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Q: Which function has a period of T? O A. y 2cosx O B. y = sin27TX O C. y = 2sinx %3D O D. Y = cos2x

A: To find the correct option.

Q: 2 x If y = x¯e" sinx,Find d

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Q: y" + 2y' – 8y = x² + cos x

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Q: Find of the following functions. [ dr (a) y = sec(7?) (b)y = sin7x + cos5a

A: here we can find the derivative as below.

Q: Q6. (A) Compute S[sec² (÷) – 1] sec*)dx. (В) Use Trigonometric substitution method to evaluate…

A: We will find the integrations as following.

Q: Find dx for the following function. 8 cos x y = 9-7 cos x xp

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Q: Q10. If f(x, y) = cos( 3x + y) Find:

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Q: f(t) = e3t + cos 6t – e3t cos 6t ; L{f(t)} =? %3D -

A: given ft=e3t+cos6t-e3tcos6t

Q: ,determine f(t−a)for the given function f and the given constant a. Q. f(t)=e−t(sin2t +cos2t), a…

A: f(t)=e−t(sin2t +cos2t), a =π/4. We need to calculate f(t−a)for the given function f and the given…

Q: (c) f(x) = ea cos(bx) for constants a and b

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Q: Differentiate the following functions: d a) dz (- 4 sec( – 10z")) = d :(V-10 cot x) dr b) d c) (- 4…

A: <math…

Q: 3 cos(wt - a), where w and a are constants

A: We find the Laplace transform

Q: Suppose z is a function of x and y, and tan Vy? +x² = ze6y. Solve for and dx ду

A: Here, given that z is a function of x and y and tan y2+x2=zxe6y⇒tan y2+x2=ex ln ze6y...(1)

Q: Graph over two periods  f(t)=4+cos(8t)

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Q: The value of 'a', for which u(x, y) = xt + ax?y2 + y is a harmonic function, is

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Q: y = C, e3x + 2C2 sin3x

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Q: az if tan Vy? +x² + z = 2*e®w. ду Suppose z is a function of r and y. Solve for

A: If x, y, z are related with a relation  fx,y,z=0 then  ∂z∂y=-∂f∂y∂f∂z