Questions from General Calculus

Q: Prove the identity. sin (π/2 + x

Prove the identity. sin (π/2 + x) = cos x

Q: Use Definition 3 to prove that limn→∞ r n = 0

Use Definition 3 to prove that limn→∞ r n = 0 when |r| < 1.

Q: If a ball is thrown upward from the top of a building

If a ball is thrown upward from the top of a building 128 ft high with an initial velocity of 16 ft/s, then the height above the ground seconds later will be h = 128 + 16t – 16t2 During what time inte...

Q: Use Definition 3 to prove that if lim n→∞ |an

Use Definition 3 to prove that if lim n→∞ |an| = 0, then limn→∞ an = 0.

Q: Use Definition 4 to prove that limn→∞ n3 = ∞.

Use Definition 4 to prove that limn→∞ n3 = ∞.

Q: Prove the identity. tan 2θ = 2 tan θ/

Prove the identity. tan 2θ = 2 tan θ/ 1 – tan2θ

Q: Prove the identity. cos 3θ = 4 cos3θ - 3

Prove the identity. cos 3θ = 4 cos3θ - 3 cos θ

Q: If sin x = 1/3 and sec y = 5

If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and π/2, evaluate the expression. sin (x + y)

Q: If sin x = 1/3 and sec y = 5

If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and π/2, evaluate the expression. cos 2y

Q: Find all values of x in the interval [0, 2π

Find all values of x in the interval [0, 2Ï€] that satisfy the equation.