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the base b of a triangle increases at the rate of 2cm per second, and height h decreases at the rate of 1/2 cm per second. Find rate of change of its area when the base and height
Fundamental Theorem of Calculus, Part II Assume f ( x ) is a continuous function on [a,b] and also assume that F ( x ) is any anti- derivative for f ( x ) . Then,
f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
Find the solution to the subsequent IVP. ty' - 2y = t 5 sin(2t) - t 3 + 4t 4 , y (π) = 3/2 π 4 Solution : First, divide by t to find the differential equation in the accu
let R be a (noncommutative) ring. Given that a,b and a+b ? R are all units, prove that a^(-1)+b^(-1) is a unit
suresh invested rs.1080 in shares of face value rs.50 at rs.54.After receiving dividend on them at 8% he sold them at 52.In each of the transaction he paid 2 % brokerage.Hpw much d
a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k
Linear functions are of the form: y = a 0 + a 1 x 1 + a 2 x 2 + ..... + a n x n where a 0 , a 1 , a 2 ..... a n are constants and x 1 , x 2 ..... x n a
Let f : R 3 → R be de?ned by: f(x, y, z) = xy 2 + x 3 z 4 + y 5 z 6 a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) . b) Brie?y
which one of the following examples represents a repeating decimal? 0.123123,1.111114,0.777777,4.252525?
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