Calculus Answers

The sum of the third and tenth term of an AP is 12. Given that the sum of the 6th terms is 3 less than one third of the eight term. Find the first term and the common difference.

Determine the monotony of the following sequences.

a) Un = 2n+3 / 5n-1 n € N

b) Un = √(n+3) - √(n+1) n € N^*

c) Un = Σ from r=1 to n (1/ n+r) , n € N

Find the area of the region bounded by the curves y= -x²/3 + 2/3x + 5 and if -x+5.

Find also the volume when the area is rotated completely about the x-axis.

Study the following functions

3) f(x) = (x³ / x-1 )s

4) f(x) = x / cube root of (x²-1)

Study the following functions

1)f(x) = Inx/x

2) f(x) = e^x-x +3

Find the general solution of these differential equations.

1) dy/dx = x/y² 2)dy/dx = x+2 / y

5) ʃ (1-sinx /1-cosx)e^x dx

6) ʃ₀^π/4 cosθ +isinθ / 2cos²θ dθ

Evaluate the following Integrals

3)  ʃ_-1¹ (x + 1/2) √(x²+x+1)dx

4)  ʃ (x+2) / √(x+3) dx