Reference no: EM132296701

Assignment Questions -

Q1. An animal skull still has 31% of the carbon-14 that was present when the animal died. The half-life of carbon-14 is 5730 years. Estimate the age of the skull to the nearest thousand years.

Q2. Solve the equation

5e^2x+1 = 4e^3x-1

for x giving an exact answer, and an approximation correct to 3 significant figures.

Q3. Consider the function f(x) = (x³-2)/(x-1).

(a) Use your calculator to find each of f(0), f(0.5), f(0.9) , f(0.99), f(1.01) , f(1.1), f(1.5), f(2) .

What do your answers suggest about the limiting behaviours lim_x→1^+f(x) and lim_x→1^-f(x)?

(b) Can you find a simple explanation? [Hint: first do a long division of polynomials.]

Q4. Consider the function g given by the rule

g(x) = (1 + (2x - 3)²)/4

For x ≥ 3/2.

(a) Find the derivative of g(x).

(b) Find the derivative of g^-1(x).

Q5. Consider the function h given by the rule

h(x) = xe^x/(x²+1).

(a) Calculate the derivative h'(x).

(b) Find the equation of the tangent line to the curve y = h(x) at the point (1, e/2) then approximate y when x = 0.9 and x = 1.1.