Use an appropriate definition to prove the following limits. g³ – 16x4 = 1 x + 2 9x² + 4 (а) lim Tt5t x2 – 25 (b) lim (c) lim = OC -3

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Q: 12. Construct an algorithm that has as input an integer n> 1,n + 1 points and xo, X1,…· Xn ... and a...

A: INPUT: n, x0,...... ,xn, x OUTPUT: ∏i=0n (x-xi)

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A: The line passes through;(x0, y0, z0)=(-1, 4, -6)parallel to direction vector:v=a, b, c= 2, -1, 0a=2,...

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Q: question Let f: {0, 1} * -→ {0, 1} * be a function that maps each string u = abc where Ja| = |b| = |...

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Q: (d) lim sin x In x x→0+ (e) lim (sec x – tan x) x→T/2- x³ – 64 (f) lim x→4 x2 + 16

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Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x2 - x - In(x) (a) Fin...

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Q: Let f(x, y) = xr sin(xy). Find (a) xy cos(xy) (b) y cos(xy) (c) x² cos(xy) (d) -x sin(xy) (e) Some o...

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Q: +-over [1, 2]. Find the exact arc length of y: - 3 4x

A: A detailed solution is given below

Q: Consider the following. 1 = (3, 7), v = (4, 6) (a) Find the projection of u onto v. 27 13 (b) Find t...

A: Given vector,u=3i+7jv=4i+6jVector projrction of u on v=u.vv2v=(3i+7j)(4i+6j)42+62(4i+6j)=12+4216+36(...

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Q: For what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable....

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Q: P = (3,7, 3) Q=(9,1,8) Find M, the midpoint of PQ: %3D

A: P=3, 7, 3Q=9, 1, 8To find M, the midpoint of PQ.M=?  

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Q: what is the derivative of hcx) at x =D0 where h lx) =2f(6)-2-VFIR) where %3D

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Q: Determine the equation (of lowest degree possible) for the graph shown You may leave your answer in ...

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Q: r.(t) = (0.5, 14.5, 0.5) + t (1,3, 3) r_(t) = (-6, 11, –1) +t (-2, 2,3) %3D Find the point of inters...

A: Given problem:-

Q: a.y = 49x" ;find (50th derivatives)

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Q: Evaluate the following integral using partial fractions: 2x2 +1 dx J(x – 1)(x – 2)(x – 3) -

A: Given: I=∫2x2+1x-1x-2x-3dx   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx ; where a is cons...

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A: Use simple integration formula for lateral surface area.

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Q: – sin x show that - In |sec x +c ??? %3D COS X

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Q: Use logarithmic differentiation to find the derivative of the function. y = x4 sin(x)

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Q: Tutorial Exercise Determine whether the series is absolutely convergent, conditionally convergent, o...

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Q: Consider the following planes. 5x + 6y – z = 66 x - 12y + 2z = 0 (a) Find the angle between the two ...

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Q: Explain why the function is differentiable at the given point. f(x, y) = x*e", (1, 0) The partial de...

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Q: Write the equation for he function graphed below. Use smallest deg 7. 5- 4- 2- 10-9 -8 -7 -6 -5 4 -3...

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Q: Find the derivative. d sin 13t dt dx 2 a. by evaluating the integral and differentiating the result....

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