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Calculus
Each side of a square is increasing at a rate of 7 cm/s. At what rate is the area of the square increasing when the area of the square is 64 cm2?
Calculus
Establish, by using limits, integration by parts and I'Hopitals Rule, whether the following integral converges:
∫ between 0 and 1, ln(x)dx
∫ between 0 and 1, ln(x)dx
Calculus
Evaluate the improper integral to show:
∫ between 0 and ∞ ,(x arctan(x))/((1 + x^2)^2) dx = π/8
∫ between 0 and ∞ ,(x arctan(x))/((1 + x^2)^2) dx = π/8
Calculus
Without using I'Hopital's Rule, evaluate the limit from t to 0 of (√(1 + t) - √(1 - t)) / t
Calculus
Q. The nth term of a sequence is given. Determine whether the sequence converges or diverges. If it converges find its limit
(i) n1/n
(ii) 2n/(2n)!
(iii) en/n
(iv) 1+1/2!+1/3!+………..+1/n!
(i) n1/n
(ii) 2n/(2n)!
(iii) en/n
(iv) 1+1/2!+1/3!+………..+1/n!
Calculus
Q. The nth term of a sequence is given. Determine whether the sequence converges or diverges. If it converges find its limit
(i) n1/n
(ii) 2n/(2n)!
(iii) en/n
(iv) 1+1/2!+1/3!+………..+1/n!
(i) n1/n
(ii) 2n/(2n)!
(iii) en/n
(iv) 1+1/2!+1/3!+………..+1/n!
Calculus
Use integration by parts to show that the integral of y/e^2y between 0 and 1 is equal to 1/4(1- 3/e^2)
Calculus
Use the reduction formula to evaluate the integral of (ln(x))^3 dx between 1 and e
Calculus
Graph each pair of parametric equations.
x = 6 sin t
y = 6 cos t, 0 ≤ t ≤ 2π
x = 6 sin t
y = 6 cos t, 0 ≤ t ≤ 2π
Calculus
Graph each pair of parametric equations.
x = 2t – 1
y = t2 + 5, -4 ≤ t ≤ 4
x = 2t – 1
y = t2 + 5, -4 ≤ t ≤ 4
