Calculus Answers

 Discuss the continuity of f(x, y) = (x^4)(y^4)/(x2+y 2)^3 if (x, y) not equal to (0,0), 0 if (x, y) = (0,0) at(0, 0) 

 A vertical line passing through the point (1,2) intersects the X axis at A(a, 0) and Y axis at B(0, b). Find area of triangle of least area if a and b are positive.

A bike drove 30 miles during a one hour trip. Show that bike speed was equal to 30 mile / hour at least once during the trip.

Find the Mean value of the function f left parenthesis x right parenthesis space equals space x cubed space minus space 3 x squared over the interval [0, 5].

X^3-2y^3+xy(2x-y)+y(x-y)+1=0

The ends and sides of a thin copper bar (𝛼 2 = 1.14) of length 2 are insulated so that no heat can pass through them. Find the temperature 𝑢(𝑥,𝑡) in the bar if initially 𝑢(𝑥, 0) = { 60𝑥 0 < 𝑥 < 1 60(2 − 𝑥) 1 ≤ 𝑥 < 2

. Find the area of the region enclosed by the graphs of y = 3/x and y = 4-x

Find the area of the region enclosed by the graphs of f(x) = x^3 and and g(x) = x^2+2x.

decide whether the function is even, odd, or

neither.

f(x) = x^4+ 3

Q.6(b) A company estimates that the demand for its product fluctuates with the

price it charges. The demand function is (05 Marks)

q= 280,000 – 400p

Where q equal the number of units demanded and p equals the price in dollars.

The cost of producing q units of the product is estimated by the function

C = 350,000 + 300q + 0.0015q2

i. Determine the number of units that should be produce in order to

maximize the annual profit.

ii. What price should be charged?

iii. What is the annual profit expected to equal?