Calculus Answers

Consider the given right triangle with legs of length x cm. and y cm. and angle θ radians. If x is decreasing at the rate of 3 cm/min. and y is increasing at the rate of 4 cm/min., at what rate is angle θ changing when x=5 cm. and y=2 cm. ?

Consider the given right triangle with legs of length x cm. and y cm. and angle θ radians. If x is decreasing at the rate of 3 cm/min. and y is increasing at the rate of 4 cm/min., at what rate is angle θ changing when x=5 cm. and y=2 cm. ?

Consider the sum A inferred by the following:

A = 1 -1/4 + 1/9 - 1/16 + 1/25...

If the 1st term is t1 = 1 and the 2nd term is t2 = -1/4, use MATLAB to determine the sum

of terms at the 57th term (i.e. including the 57th term). Give answer to 4 decimal places. Also, provide MATLAB code.

Determine which of the following functions are of bounded variation on[0,1]

a. f(x)= x^2sin(1/X) if x#0 ,f(0)=0

b. f(x)= √x sinx,if x#0,f(0)=0

Write the polynomial function of minimum degree in standard form with real coefficients whose zeros include 1,1-i ,1=i ?

Let f(x) = x² and g(x) = ^x+1

____

^x+3

1. Evaluate(f °g)(2)

2. Find formular for (f ° g) (x)

Suppose that f is an odd function with domain R. It is know that f(4) = -5. Find f(-4).

Given the function, f(x,y) = x^3 y + 12x^2 - 8y Find all critical points and classify each as a local maximum, local minimum, or neither.