Evaluate the following limit using l’Hôpital’s Rule. limx→0 2 sin 7x/5x Use l’Hôpital’s Rule to rewrite the given limit so that it is not an indeterminate form. limx→0 2 sin 7x/5x = limx→0 ( Evaluate the limit. limx→0 2 sin 7x/5x = (Simplify your answer.)
Find the following limit. lim x→0+ (2x csc(π - x)) lim x→0+ (2x csc(π - x)) = 2 (Simplify your answer.)
The integral in this exercise converges. Evaluate the integral without using a table. ∫0 ∞ dx/x^2+64 ∫0 ∞ dx/x^2+64 = π/16 (Type an exact answer, using π as needed.)
The integral in this exercise converges. Evaluate the integral without using a table. ∫0 11 dx/√121-x^2 ∫0 11 dx/√121-x^2
The integral in this exercise converges. Evaluate the integral without using a table. ∫-∞ ∞ 2xdx/(x^2+1)^16 ∫-∞ ∞ 2xdx/(x^2+1)^16 = 0