Calculus Answers

what is the limit of cosx-2sinx over cosx+2sinx as x approaches to π/2.

Find the equations of tangent and normal to the curve y=4x-x^2 at (1,3)

Use the techniques of differentiation to find dy over dx
(i) 3e to the power x = xy+xsquared +ysquared
(ii) y= 2xcubed over (xsquared - 4)squared

Find the area bounded by the curve y = |x−1|, the x-axis and the lines x = −7 and x = 11

1. Find the area bounded by the curve y=| X-1 |, the x-axis and the lines x =-7 and x= 11

find the working application with derivation and upload the same here, with the same application answer the bellow mentioned question.

1) how does the above application is working with derivation?

2) which Derivation method is used in the same?

3)can we use any other method in the same application if yes which and if no why?

find the working application with derivation and upload the same here, with the same application answer the bellow mentioned question.

1) how does the above application is working with derivation?

2) which Derivation method is used in the same?

3)can we use any other method in the same application if yes which and if no why?

The rate of change of the value of an investment, S, with respect to time, t ≥ 0, is given by dS dt =1000r 10ert/100, where r is the annual interest rate (assumed constant) and the principal of the investment is S(0) = 10 000. (a) Find an expression for S(t), that is, the value of the investment at time t. (6 marks) (b) Verify that your expression for S(t) is correct by computing S(t). (1 mark) (c) Explain why S(t) is continuous for t ≥ 0. (1 mark) (d) Determine, by computing lim t→∞S(t), what would happen to the value of the investment if t were to grow without bound. Interpret the result. (5 marks) (e) How long would it take for the value of the investment to be exactly 15 000? (4 marks)

Find the area bounded by the curve y = |x − 1|, the x-axis and the lines x = −7 and x =11. (5 marks)

2. Let f be a continuous function on the interval [a,b], and let c = a+b/2 suppose that F is any antiderivative of f with F(a) = 1 and F(b) = −2. Find: (a) ba f(x)dx (2 marks) (b) −abf(x)dx (2 marks) (c) ca f(x)dx + bcf(x)dx (2 marks) (d) Dx[−(caf(x)dx + bcf(x)dx)] (2 marks)