Calculus Answers

a and b are vectors defined by a=8i+2j-3k and b=3i-6j+4k, where i,j,k are mutually perpendicular unit vectors. Calculate a and b.

An artificially created lake is bordered on one side by a straight dam. The shape of the lake surface is that of a region in the xy-plane bounded by the graphs of 2y=16-x^2 and x+2y=4. Find the area of the surface of the lake.

Calculate the area of the bounded region between the curves y^2=x and 3y = -3y + 9 ?

Show that if x is small, the [removed](1+x)/(1-x))^0.5 is approximated by 1+x+0.5*x^2..This sum is
related to binomial expansion and there is a hint provided at the end of the question-that is,MULTIPLY BY ((1+x)/(1-x))^0.5 FIRST.

please provide me some problem, where third derivative or more than is used to find maxima and minima. and please solve one problem like this.

what is the graph of y=x+(1/x). i can't sketch the graph.because if i use x=0 then y=infinity.

and i want to find maxima and minima of the function. here the maxima is less than in minima. but don't understand why this happens? please show me the maxima and minima in graph.

integral sqrt(1-x^2) . sin^-1 x dx

integral sec^-1 x dx