Find the harmonic function w(x, y) = ax2 + bxy + cy2 , in cartesian coordinates, that takes the values cos(2θ) on the unit circle.

Q: Approximate (a) cos 0.8 and (b) cos 1/2 using the linear approximation technique

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Q: Find the speed at the given value of t. r(t) = (sin(3t), cos(6t), cos(7t)), t = " 2. II

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Q: Consider the function 3..2 f(x, y) = cos(rxy) – a°y?. = cos(Txy) – x°y°. a) Find the equation of the…

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Q: T For y = 5 cos ( 4x 3 - its amplitude is its period is its horizontal shift is

A: Given  y= 5cos(4x-π/3)  We have to find its  1) Amplitude 2) Period  3) horizontal shift

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t. x-…

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Q: What is the equation of the line tangent to the curve ev + cos(x) = 1 at the point (,0*? Y = 0 A B…

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Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0S0< x.…

A: Given :           r=6 cosθ

Q: Let y = (sin x+ cos r)e , x E 0, 27. Then the x coordinates of the inflection point(s) of this…

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Q: Find the slope of the curve 2xy = In(e2*) sin(x) at the point (2,2)

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Q: Use the value of the given hyperbolic function to find the values of the other hyperbolic functions…

A: We use the following identities to find values of other hyperbolic functions:

Q: Find dy/dx of the function. y=cot-1(4-3x2)

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Q: Differentiate y with respect to x where y= cos(-3x2)

A: Differentiate y with respect to x.

Q: Find the extremal of the functions using Euler's equation. [²(x² + y² (y2 + y² + 2ye*)dx, y (0) = 0,…

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Q: Find the differentiation and provide complete solution a. y= cos3x2 b. f(t)=sin34t

A: a) y=cos3x2 On differentiation: dydx=-sin3x2×3×2xdydx=-sin3x2×6xdydx=-6xsin3x2

Q: (c) Show that the function z -- eX sin yt ey cos

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Q: The slope of the tangent to the curve r = 3 sin 40 at 0 = 0 is %3D Şelect one: O a. -1 3D1 O b. 0 C.…

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Q: C) Find the equation of tangent to the curve 4x +9yi = 36 at the point (3 cos 0, 2 sin 0).

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Q: Find d-/dx² at the given point without eliminating the parameter. x=0+ cos0 and y=1+sin0 ; 0 =a/6,

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Q: At what points the curve x = 2a(cos(t))-a(cos(2t)), y = 2 a(sin(t))-a(sin(2t)) has vertical and…

A: Given: The curve equations are shown below. x=2acost-acos2ty=2asint-asin2t Calculation:…

Q: Find the tangent to y = cos x at x = 5- O A. y=x+7 O B. y= -x+7 O C. y= -x-7 O D. y= 1

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Q: Differentiate the function. y = (cos(4x))*

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Q: A. Find the derivative of the function at o P in the direction of A f(x, у) — х — V3sec-1(2xy)at…

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Q: Find dy and evaluate when x = T and dx 0.5 for the function y -10 cos (5x)

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Q: 4. Find when dx tanx a. y e, giving your answer as a function of y. b. y- In(xvx-1), x> 1 sinx-cosx…

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Q: The derivative dy for the function %3D (1i) y= cot リーCof V-x

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Q: 30 Find the real and imaginary parts of the functions (a) z²e2= (b) sin 2z Verify that they are…

A: We will use standard techniques.

Q: Find the vertical trace of the function at x = 1: g(x, y) = cos√x² + y²

A: Definition : Consider a function z=f(x,y) with domain D⊆R2. A vertical trace of the function can be…

Q: if y^3 + y = 2 cos x, find the value of d2y/dx2 at the point (0, 1).

A: Given,

Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+2…

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Q: Find the direction in which the function g(x, y) = cos(xy) decreases fastest at the point (1, pi)

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Q: Find the speed (as a function of t ) of a particle whose position at time t seconds is c(t) = (sin t…

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Q: Sketch the curve. And indicate the direction of increasing T at T =0

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Q: 2. Consider the squiggly graph of all points (r, y) that satisfy sin(re") = a + y. 1 Using implicit…

A: Given, sinxey=x+y

Q: Find the value of zrr at the point (0, 3, 2) where x?y? + z2 – cos(xyz) = 10. -

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Q: Use the tangent equation. tollowing equation to find the approximation at Co,0): fCX.y)e Jy+ cos cx)…

A: The given function is: f(x,y)=y+cos2x

Q: Let a function y(x) be given implicitly by the formula: y° - 3xy2 +y cos(x) – x = 10. %3D Find the…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y) = - 5xy + 2y. Po(-7,1), A=…

A: Given query is to find indicated derivative.

Q: Find the equation of the tangent plane to z = e9 +x + x³ + 6 at the point (3, 0, 253).

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Q: x = 6 sin t, y = t +t at t = 0.

A: Let's find.

Q: At what point does the sine function y = sin x, cross the y axis? O (T, O) O (0,0) O (1,0) O (0,1)

A: Given  function is y=sinx. We have to find the point at which the function y=sinx cross the y-axis.…

Q: Find the exact length of the curve. y = (x-x2)1/2 + sin-1((x1/2))

A: The arc length formula is given as

Q: Find the value of zr» at the point (0, 3, 2) where a²y² + 2² – cos(ryz) = 10.

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Q: Find the derivative of the function at Po in the direction of A. f(x,y) = - 3xy - 3y, Po(2,4), A= -…

A: We have to find out derivative

Q: Let a function y(x) be given implicitly by the formula: y3 − 3xy2 + y cos(x) − x4 = 10. Find the…

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Q: For what value(s) of x in the interval -15 sxs -5 will the sinusoidal function shown below have a…

A: By definition, a function is a special case of a relation between the members of two sets. It is a…

Q: Find the slope of the graph of cos(x + y) = 2x at the point ( 0, T1/2 ). Hint: Differentiate…

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Q: Please solve the Vƒ of the function below at point P. a) f = (x² + y² + 2)-05, P; (12,0, 16) b) f =…

A: a) The given function is f=x2+y2+z2-0.5. This gives ∂f∂x=-0.5 x2+y2+z2-0.5-1…