Calculus Answers

d/dx[(x^2+1)^sinx] .

1. Find the volume of the parallelpiped spanned by the vectors~A= i+j-k;~B=i-j+k;~C=-i+j+k

2. Assume that~A=<ax, 0, 0>;~B=<bx, by, bz>; and ~C=<cx, cy,cz>, and demonstrate that the following vector identity holds: Ax(BxC) = (A.C)B-(A.B)C

Note that if you replace the subscript "x" by "I","y" by"j", and "z" by "k", and then cycle x->y->z->x appropriately, you've proven the identity is true in general.

3. What is the cosine of the angle between the plane x+y+z= 5 and any of the coordinate planes? What about the cosine of the angle between x+y+z= 5 and x+ 2y+ 3z= 5?

4. What is the distance between the point (1, -2, 4) and the plane 3x+ 2y+ 6z= 5?

5. What is the distance between the parallel planes ax+by+cz=d1 and ax+by+cz=d2? You may wish to try picking a point on one plane that you can specify exactly and working out the distance from that point to the other plane.

In order to receive bonus pay for summer work, Kelly has to work at least 60 hours in her online course. Due to other commitments, she is unable to work more than 120 hours. Use set notation and interval notation to represent the number of hours she can work in the online course.

differentiate log(1+x^2) with respect to tan^-1(x)

use simpson’s method to approximate limit 0 to 8 ∫ (x^2-x+3)dx with 8 sub-intervals.

Find the angle between the curves y^2=ax and ay^2=x^3
(a>0
), at the points of
intersection other than the origin.

Let f(x)={x^2-16x,x<9}{12√x,x>=9}if f continuous at x = 9 ? Determine whether f is  differentiable at x = 9 . If so, find the value of the derivative there.

evaluate limit 6 to 0 ∫ f(x)dx if f(x){x^2,x<2,3x-2,x>=2}

prove that cosx>=1-(x^2/2)for all x in the interval[0,2π]