(a) Use the complex exponential to prove the double angle formula cos2 -sin2 a cos(2.ar) . (b) Use the complex exponential to evaluate the indefinite integral sin(4t) dt.
(a) Use the complex exponential to prove the double angle formula cos2 -sin2 a cos(2.ar) . (b) Use the complex exponential to evaluate the indefinite integral sin(4t) dt.
Problem 5: Evaluate: sin #2? + cos2 9 (2-1)(2-2) where C is the circle z = 3.
A-6 945 How to show these results? You may need to use Parseval's idenity. Esplain it when used.
3. (a) Use the Weierstrass M-test to show that the series Σ V1 – cos2 (nx) 1+ n2 n=0 represents a continuous function on R.
1. Evaluate the integral of f(r, θ, φ)-1 + r2 cos2( over a sphere of radius h. (Hint: we did most of this problem in class; 9) sin φ
1. Evaluate the integral of f(r, θ, φ)-1 + r2 cos2( over a sphere of radius h. (Hint: we did most of this problem in class; 9) sin φ
on [0, 2T). sin x 2 2 cos2 Find all solutions to 1 _ Enter the answer in terms of T, as needed. Do not enter a decimal approxima Click here to open instructions for entering a. This question accepts lists of numbers or formulas separated by semicolons. E.g. "2; 4; 6" or "x+1; x-1". The order of the list doesnt matter but be sure to separate the terms with semicolo
(3) Evaluate the indefinite integral. ſtan(x) + cos2 (2) dx cos(2)
Solve the equation 4 cos2 x - 1 = 0 on the interval (0,21).
Find all points on the graph of the function f(x) - 2 cos(x) + cos2(x) at which the tangent line is horizontal. (Use n as y (x, y) = (smaller y-value) (,Y) = (larger y-value)
9. A rigid tank contains 67.5 g of chlorine gas (Cl2) at a temperature of 78 °C and an absolute pressure of 5.30 x 10 Pa. Later, the temperature of the tank has dropped to 31 °C and, due to a leak, the pressure has dropped to 3.90 x 10 Pa. How many grams of chlorine gas have leaked out of the tank? (The mass per mole of Cl2 is 70.9 g/mol.) X9.19196 8