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...

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...

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...

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

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.

Evaluate I =⌠⌠FdS , where F( x,y,z) = x^3 i + y^3 j + z^3 and S is the surface of the solid bounded by the hemisphere z =sqrt(1-x^2-y^2)and the plane z = 0

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

Evaluate the definite integral a ∫−2x√(x^2+a^2) dx -a

Evaluate the definite integral 1 ∫ x^2√(4x+8x) dx 0

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...

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

If f(x)=1x+2, find f′(−5), using the definition of derivative. f′(−5) is the limit as x→_____ of the expression __________ The value of this limit is _________

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?

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

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

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

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...

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

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

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