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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
The remainder when 5^99 is divided by 13 Ans) 8 is the remainder.
Consider the wave equation utt - uxx = 0 with u(x, 0) = f(x) = 1 if-1 ut(x, 0) = ?(x) =1 if-1 Sketch snapshots of the solution u(x, t) at t = 0, 1, 2 with justification (Hint: Sket
A lotus is 2m above the water in a pond. Due to wind the lotus slides on the side and only the stem completely submerges in the water at a distance of 10m from the original positio
128sinpower8=cos8-8cos6+28cos4-56cos2+35
81-3/4
A building is in the form of a cylinder surrounded by a hemispherical vaulted dome and contains 41(19/21-) cu m of air. If the internal diameter of the building is equal to its t
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). Hence, a ∫ b f(x) dx =
Solve -10 cos(3t )= 7 on [-2,5]. Solution Let's first get the inverse cosine portion of this problem taken care of. cos(3 t )= - 7/10 ⇒ 3t = cos -1 ( - 7
Find the third vertex of a triangle if its two vertices are (-1, 4) and (5, 2) and mid point of one side is (0, 3).
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