Use a graphing utility to complete the table and graph the functions in the same viewing window. Use both the table and the graph as evidence that y₁ = y2 Y₁ = sec(x) = cos(x), y₂ = sin(x) tan(x) 3.0 3.8 X У1 Y2 Verify the identity algebraically. 4.6 5.4 6.2 7.0 7.8

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Q: (15) Let 0 € (0,) and cos(0) = . Find sin(0) (Hint: sin² 0 + cos² 0 = : 1). (SHOW YOUR WORK)

A: Given data

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A: NOTE: Refresh your page if you can't see any equations. . it is given that,  so choose the equation…

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Q: (16) Perform the following calculation and simplify. 1 3 1 I 43 3

A: 1-1343

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A: fx,y=ln5+x2y2

Q: 1 5)Test for Convergence: '[ln(n)]²n n=3

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A: F→x,y=5+8xy2i+8x2yj

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Q: 43. Find the gradient of the function f(x, y, z) = x²e»²².

A: we need to find the gradient  of function f(x,y,z) =x2eyz2

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Q: Consider the vector field F = Evaluate r(t) = t²i+t³j, 0≤ t ≤ 2 LE F-dr along the curve C:

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A: This is question related to area of integration which is application of definite integral.

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A: given,  f(x,y)=e2xsin(3y)given,  ∇f(x,y)=(fx(3,1),fy(3,1))

Q: Consider the function f(x) = 2x^3 - 3x. a) Find f'(x) using the definition of the derivative.

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