Find a such that the distance from (−1, 2) to ax − y + 9 = 0 is √5 units.

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Q: the

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Q: 1. Find the minimum amount of fencing required to surround a rectangu- lar area of 100 square feet.

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A: Given, y=x2+42x

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A: By using Chain Rule, to find ∂u∂x, ∂u∂y, and ∂u∂z at x, y,z=π4, 12, -12.u=eqr sin-1 p, p=sin x, q=z2…

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Q: 2x + [2x] x+ 2+ x² + x - 2 Evaluate lim 2x+ [2x] x+ 2 x²+x-2 and lim

A: Given information limx→-2+ 2x+2-xx2+x-2     and    limx→-2- 2x+2-xx2+x-2.

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Q: x 6 ♥ 5.5 5.1 5.01 f(x) Based on ONLY the table of values above, what conclusion c lim f(x) = 10.…

A: Topic:- application of derivatives and limits

Q: Q3. Use the chain rule method to find dt If (z=x. y), where x = cos (t) and y=sin (t)

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Q: Q5. Find the directional derivative of the function [f(x, y, z) = xy + y.z+z.x] at the point…

A: Given fx, y, z=xy+yz+zx Point P0=1, -1, 2 Equation of the line is x-310=y-211=1-z2

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Q: Sketch the level curves of g(x, y) 1- y² x² where k € {-1,0, 1}

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Q: Find a value of h for which y 3.0 2.5 2.0 1.5 1.0- 0.5 0.5 ƒ(2 + h) − ƒ(2) h 1.0 1.5 = 0. f(x) 2.0…

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Q: Given that f(x) = (x-7)2 and g(x) = 7 - 4x, find: a) (f + g)(-3)- b) (f-g)(-3)- c) (fg)(-3)- d)…

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Q: 2. Use the different differentiation rules and formulas to determine the derivative of the following…

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Q: Prove that (x₁, y₁), (x2, y₂), and (x3, Y3) are collinear points if and only if X1 Y1 1 2 Y2 3 y3 1…

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Q: Multivariate Calculus

A: We have to find the region bounded by the curves:x+y=2 ,  x=0 , y=0.Here x+y=2⇒y=2-x⇒y=(2-x)2…

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Q: 4. A. Find the parametric and Cartesian equations of the line connecting the points A (1, 2, -1) and…

A: Given two points are A(1,2,-1)   and B(-1,0,1). The cartesian equation of a line passing through two…

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Q: 2x + [2x] ate lim x+ 2+ x²+x-2 and lim x+ 2 2x + [2x] x²+x-2

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Q: following limits, if they exist. lim (x,y) →(0;0) x³ + x²y + 2y³ x² + y² ;

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Q: Find the horizontal asymptotes of g. g(t) = 10 13+ 4-1 (Give your answer as a comma-separated list…

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