Pr. #14) Find and sketch the domain of the function in R2. In [sin- ()] (x, y) x2+y² %3D -

Q: Find the equation of the tangent plane to the graph of f(x, y) = In (14x² – 11y) at the point (1,…

A: Let us considre a two variable function z=f(x,y)  Then the equation of tangent plane  at (a,b) is…

Q: Verify that if y = ƒ(θ2 sin θ, then y'(θ) = ƒ'(θ) sin θ + ƒ(θ) cos θ.

A: We use the product rule

Q: Example: show that u(t)=sin t i + cos t j+ 5k has constant length and is orthogonal to its…

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Q: DO NOT include spaces in between characters. Determine the domain of y = sin (x – 1).

A: To find the domain of y=sin-1x-1

Q: „Show that the complex variable function below is differentiable analytic only at origin point? f(z)…

A: We will show the required result.

Q: a) Use the definition of the hyperbolic functions to prove that 2cosh?(x)–1=cosh(2x). 1%3D

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Q: Let r be a positive real number. The equation for a circle of radius r whose center is the origin is…

A: Given equation: x2+y2=r2                     . . . (1) (a) Differentiating (1) with respect to x,…

Q: Find the maximum value of sin θ + cos θ.

A: Let  fθ=sin θ+cos θ Differentiate with respect to 'θ', we get f'θ=cos θ-sin θ For maxima or minima,…

Q: Which of the following is the tangent equation drawn to the pi/4 point on it? y = 25 - tanx curve…

A: This question is based on straight line. The general equation of a straight line is            y =…

Q: 34 10- Find equation of tangent line at the point (0, T) for Cos (7x- y) %3D 4y

A: Solved below

Q: Using the parametric differentiation find dy, if x = 9t², y = 5t³ O 0.83t O 1.11t O 2.70t O 1.39t…

A: x=9t2 ,y=5t3

Q: Show that the function y = x¹/², x > 0, is strictly concave

A: Given that y=x1/2 Differentiate both sides w.r.t x, y'=12x1/2-1y'=x-1/22 Again differentiate w.r.t.…

Q: Determine where the following function is differentiable? Where is it holomorphic? Determine the…

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Q: The slope of the tangent line at any point (x, y) on the curve 3x2 -2x+7 and the point (1, 3) is on…

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Q: 3 Ay 10- Find equation of tangent line at the point (0, 7) for Cos (7x - y)

A: Solving

Q: 12. Determine an equation for the sinusoidal function shown: ✔✔✔ (-4x/3, 2) - دان LAT (580, 4)…

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Q: 6) By implicit differentiation find a) xy + y² = 2 find d²y/ dx² %3D b) sin(x²y²)= x find dy/dx

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Q: e points of inflections and the local maximum and minimum values of the function y=2sinx + sin2x in…

A: In this question, the concept of maxima and minima is applied. Maxima and Minima The extrema of a…

Q: Suppose that a curve is given by the equation y2=x2+x+1 which defines y as function(s) of x Find…

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Q: Differentiate the given function. y=XV8X-5 y'= (Type an exact answer, using radicals as needed.)

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Q: 7. Use implicit differentiation to find two equations between x and y such that the tangent line to…

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Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

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Q: Suppose f"(x) =Osin(3z) and f'(0) 4 and f(0) =-2 f(T/3) = Note: Dont confuse radians and degrees

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Q: Differentiate the function. P'(W) = P(w) = 6w² - 4w+2 √w W

A: To differentiate the following function.