MT129 Calculus and Probability Assignment

Assignment Help Mathematics

Reference no: EM132571056

MT129 Calculus and Probability - Arab Open University

Question 1: Letf(x)=x^2+1 and g(x)=1-x.
Find f(g(x)). Simplify your answer.
Find g(f(x)). Simplify your answer.
Describe the domains of f(x),g(x)and f(g(x)).
Are there any values of xsuch f(g(x) )=g(f(x))? Justify your answer.

Question 2:
Use the definition of the derivative to find s'(1)if s(x)=√x.
Use the definition of the derivative to find f'(x)if f(x)=3/x^2 .

Question 3:
Find an equation of the tangent line to the graph of y=(2x-1)/(1-x^3 ) at the point whose x-coordinate is 0.
Find an equation of the tangent line to the graph of f(x)=(x^2-3)^5 (2x-1)^3 at the point whose x-coordinate is 2.

Question 4: Find the points on the graph of x^3+y^3=3xy at which the tangent line is horizontal.

Question 5: Letf(x)=3x^5-5x^3.
Find the intervals on which f is increasing or decreasing.
Find the local maximum and minimum of f, if any.
Find the intervals on which the graph of f is concave up or concave down.
Find the points of inflection, if any.
Sketch the graph of fon [-2,2].

Question 6: Find two positive number x and y such x+y=30 and xy^2 is maximum.

Question 7:
Solve for x the equation ?27?^x+3^(x+3)=4·3^(2x+1).
Using logarithmic differentiation, find the derivative of
f(x)=(e^(-3x) √(2x-5))/?(6-5x)?^4 .

Question 8: Let h(t)=2/(1+3e^2t ).
Show that h is decreasing for all t.
Find the point of inflection for h.

Attachment:- Calculus and Probability.rar

Reference no: EM132571056

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