The velocity v m s –1 of a particle at time t seconds, is given by v = 2t + cos2t, for 0 ≤ t ≤ 2. (a) Write down the velocity of the particle when t = 0. When t = k, the acceleration...

The velocity v m s –1 of a particle at time t seconds, is given by v = 2t + cos2t, for 0 ≤ t ≤ 2. (a) Write down the velocity of the particle when t = 0. When t = k, the acceleration...

Question 1: 1. Given a cycle of radius 2, we put inside it 13 squares with all fours sides being 1 Show that there are at least 2 squares that share a point. Remake The area of a cycle of radius...

F=e^y i+(xe^y+e^z)j + (ye^z)k evaluate ⌠Fdr along A(0,2,0) and B(4,0,3). Find if its conservative and if so find its potential then use A and B.

what values for length and width give the maximum area if the perimeter is 100

Use Newton's method to approximate the indicated root of the following equation correct to six decimal places. The root of 2x^3−6x^2+3x+1=0in the interval [2,3].

Helium is pumped into a spherical balloon at a rate of 5 cubic feet per second. How fast is the radius increasing after 2 minutes? Rate of change of radius (in feet per second)...

Evaluate the given indefinite integrals. a) ∫ a dx=_____+C b) ∫ t^2 dx=_______+C

Evaluate the definite integral (if it exists) 2 ∫ −1x(√x-1) dx 1

List the critical numbers of the following function in increasing order. Enter N in any blank that you don't need to use. G(x)=^3√3x^2-3x The square root is over everyt...

The top of a 17 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 4 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom...

Find f if f′(x)=6x−[3/x^4], x>0, and f(1)=3. f(x)=_____

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 9 mi^2/hr. How rapidly is radius of the spill increasing when the area is 9 mi^2?

Find dy/dx in terms of x and y if ^4√x=3√y. dy/dx=_____

Find the derivative of w=(√t+5)^76 dw/dt=______

Find the derivative of f(x)=√[6−sinx/2−cosx] The square root is over everything. f'(x)=____

Find f if f′′(x)=sin x + cos x, f′(0)=3, and f(0)=2. f(x)=_____

If you have 140 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose? Area=_______

Evaluate the following limit lim [8−√x]/[8+√x] ...

Find the inflection points of f(x)=8x^4+110x^3−42x^2+13. (Give your answers as a comma separated list) Inflection Points=_______

Find all critical points of the function f(x)=x^3+7x^2−7x−3. If there is more than one critical point, list them in descending order and separate them by commas. Critical...