Calculus Answers

lim (e^tanx - e^x)/ (tanx -x )
x tends to 0

solve it

lim (e^tanx - e^x)/(tanx- x)
x-0

During an automobile sale, cars are selling at the rate of 12/x + 1 cars per day, where x is the number of days since the sale began. How many cars will be sold during the first 7 days of the sale?

calculate:
1) lim 1-cos x/x+x^2 2) lim x-2x^2/3x^2+5x 3) lim (x sin 1/x)
x->0 x->∞ x->∞

4)Show that the sequence 1/2, 2/3,3/4,4/5,... is strictly increasing sequence.

Determine whether each of the following converges or diverges:
∞
1)∑ 1/n^2+1
n-1

∞
2) ∑ 2^n+5/3^n
n-0

∞
3) ∑ sin k/k^2
k-1

Evaluate

1) ∫∫ (3x+4y)dydx over the region R enclosed between the curves x=y^2 and y=x^2
R

1 x^2
2) ∫ ∫ y^2x dydx
0 -x

Given the triple integral ∫∫∫(x^2+y^2)^1/2 dxdydz
s

S={ (x,y,z): 1≤ x^2+y^2 ≤4, x≥0, y≥0, 0≤ z ≤2}

Sketch the solid S and evaluate the integral.

Find the Taylor’s Polynomial of degree n about x = c and the remainder for the function f given
1)f(x)=1/3x+4 and c=0
2)f(x)= sin x and c= π/6

1. The point of inflexion of the curve y = x4 is at a. x = 0 b. x = 3 c. x = 12 d. No where
2. y = x3 – 3x2 + 3x + 7 has a. A maxima b. A minima c. Both maxima & minima d. None
3. y = x2 – 6x + 13 has a. A maxima b. A minima c. Both d. None
4. In question above, the extreme value of y is a. 4 b. 3 c. -4 d. -3
5. Evaluate the integral of ∫x.ex dx
6. ∫log x^2 dx is equal to
7. Integer x^2ex a. ex (x2 – 2x + 2) b. ex (x2 + 2x + 2) c. ex ( x + 2)2 d. none
8. Evaluate ∫ex (x3 + 3x2) dx a. ex + 3x + c b. e3x + 3x + c c. ex. X3 + c d. e3x + 3x + x3 + c
9. the equation of the curve which passes through the point (1, 3) and has the slop 4x – 3 at any point (x, y)
10.the equation of the curve in the form y =f(x) if the curve passes through the point (1, 0) and f’(x) = 2x – 1 is