Calculus Answers

define f : X → Y, g : Y → Z and h : Y → Y

Find the tangents and normals to the curve
xy+2x-y=0
that are parallel to the line
2x+y=0
Draw the graphs showing the tangents and normal to the curve.

Section 6.1, Question 007

Find the area. Show the exact answer

1. 7x^2, y=7 square root of x, x= 1/4 and x=1

2.y= cos5x, y=0, x= pi/10, x= pi/5

3. y= e^x, y= e^5x, x=0, x= ln 2

1-the curve y=x^2+A÷x has the gradient of 8 when x =5.calculate the value of A.
2-find the maximum point and the minimum points of :y=2x^3-3x^2-12x+1.

Find the derivatives of
1.y=3x^2-5x+5
2.f (x)= x+x^2÷2+x^3÷3

Use an appropriate scale to draw each vector. Lable the magnitude, direction and scale:
a) momentum of 50 kg•m/s south b) velocity of 15 km/h at a bearing of N30°E

Draw two non-collinear vectors

The acceleration of an object moving in a strange way has been modelled as a = e^x x.

A) use integration by parts to find an equation to model the velocity v if v = ∫ e^x x dx (the x is the letter x not multiplication)

B) is the problem any different if you find v = ∫ xe^x dx?

A complex function can be modified by the equation: y = cos(x^3) 3x^2
Find the indefinite integral of the function ( ∫ cos(x^3)3x^2 dx) using a substitution method?

For the function v = 12 sin 40, calculate the: a) mean b) root mean square (RMS)
Over a range of 0 ≤ Ø ≤ π/4 radians.

(Note: the trigonometric identity cos 2Ø = 1-2sin^2 Ø)