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1. A ladder 20 ft long leans against a vertical building. If the top of the ladder slides down at a rate of p 3 ft s, how fast is the bottom of the ladder sliding away from the building when the top of the ladder is 10 ft above the ground?
2. A sphere is growing in such a manner that its volume increases at 0:2 m³ s(cubic meter per second). How fast is its radius increasing when it is 7 m long?
Evaluate through constructing table of values
Lim In x 1-cos t/sint
t→0
Write down 𝑇3(𝑥), 𝑇4(𝑥), 𝑎𝑛𝑑 𝑇5(𝑥) for the Taylor series of 𝑓(𝑥) = ln (3 + 4𝑥) about 𝑥 = 0
Specify and sketch the domain of the following function
f(x,y)= (y^2 + x^2) / √(y^2 - x^2)
If the power series ∑
∞
n=0
n
n a x converges uniformly in [, ]α, β then so does . ( )
∑
∞
=
−
n
n
n a x
True or false? Justify.
Sketch the curve y = x3-3x.
Find the equations of the tangent and the normal of y = 3x2-2x+1 at point (1,2).
Find the first derivative of y with respect to x. Use the given relation in its
implicit form.
a. x2 + y2 = a2
b. X2 + 4y2 = 4ay
Find the second derivative of y = (x2+x+1)2
Find the first derivative of y = (3x+4)2
