Calculus Answers

Determine the set of interior points, exterior points,

accumulation points, isolated points, and boundary

points of the set E = {x : x

2 ≥ 2}.

If the net investment function is given by I (t) = 100e^ {0.1t} calculate

(a) The capital formation from the end of the second year to the end of the fifth year;

(b) The number of years required before the capital stock exceeds $100 000

Find the consumer's surplus at $P = 5$ for the following demand functions:

(a) P=25-2Q,

(b) P= 10/sqrt {Q} 

Find area bounded by f(x) =x^2 and g(x) =x+2

Find the area of the region between the x-axis and the graph of f(x) from a=-1, to b=2, if f (x)=e^2x+3

A particle moves along the space curve r=e-t(cos⁡t i+sin⁡t j+k). Find the magnitude of the veloctiy at any time t.

Select one:

A 5e-1

B 5e-t

C 3e-1

D 3e-t

Evaluate the following limits,if they exist,where [x] is the greatest interger function

a)lim [2x]/x as x approaches 0

b)lim x[1/x] as x approaches 0

If u=x(1-y) and v=xy, then find the value of the Jacobian ∂u,v∂(x,y)

Select one:

A -x

B x2

C -x2

D x

If the demand function is P = 70 - Q find an expression for TR in terms of Q.

(1) Differentiate TR with respect to Q to find a general expression for MR in terms of Q. Hence write

down the exact value of MR at Q = 60.

(2) Calculate the value of TR when

(a) Q=60 

(b) Q=61

and hence confirm that the 1 unit increase approach gives a reasonable approximation to the exact value of MR obtained in part (1).

Find an equation of the tangent line to the curve 𝑦 = 2𝑥 2 + 3 that is parallel to the line 8𝑥 – 𝑦 + 3 = 0