Calculus Answers

Conside the function f(x)=x to the power 4-2xcube+2x-1

A. Find the critical points of f(x)

B. Determine the interval over which f(x) is increasing and the interval on which it is decreasing.

Lim_x→0 (x cos x)

a) Find an equation of the tangent line at the origin to the curve .

1+sin(x+y)=xy+cosy

Consider the telescoping series

"n"

"Sn = \u03a3" "[ ( 1 \/ (k+1) ) - ( 1 \/ k )" ]

"k=2"

Which of the options below are incorrect?

1) "Sn = [ (1-n) \/ ( 2n + 2) )" ]

2)

"n + 1"

"Sn" = - "\u03a3 [ 1 \/ k ( k - 1) ]"

"k = 3"

3)

"n"

"Sn = \ufeff\u03a3 [ 1 \/ k ( k + 1) ]"

"k = 2"

4)

"\u221e"

"Sn = \ufeff\u03a3 [ 1 \/ k ( k + 1) ]" = "1\/2"

"k = 2"

5)

"\u221e"

Sn = "\u03a3 [ 1 \/ k ( k - 1) ]" "= - 1\/2"

"k = 3"

a ball is thrown down from the top of a 210-ft building with an initial velocity of -24 ft per second. the position function is s(t)= -16t^2+v_ot+s_o.

what is the velocity of the ball after 1 second.

find the rate of charge of y with respect to x on the internal [-2,2], where y=3x^2-2x

3. Argue for or against using a continuous function to model each of the following scenarios (it is not necessary to find equations). (6 marks)

a) the cost of filling a car’s tank with fuel

b) the fines for speeding on a highway

c) The temperature in an oven as it warms, cooks food, and then cools 

Derive a reductions formula for integral e^mx/xⁿ dx , where m and n are constants.

Let D: {(x,y)| x>0, y>0}. Consider two function f and g from D to R, defined by:

f(x,y) = Inx - Iny and g(x,y)= x^2+ 3y^2/(2xy)

Show that the necessary condition for the functional dependence of f and g is satisfied. Also find a functional relation between f and g.

A particle is executing Simple Harmonic Motion of amplitude 6 m and period 3× 5

seconds. Find the maximum velocity of the particle.

Differentiate the following functions with respect to x (i) sinh x tanh x (ii) Z x √ x sin t t dt.