Please help!!!

Please help!!!

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...

Let \displaystyle g(x)=\int_0^x {\sqrt{1+6 t}}\,dt. Use the Fundamental Theorem of Calculus to find g'(x).

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

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

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.

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...

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

For the function f(x)= {x^2−4, 0≤x<3 f(x)= {−1, x=3 f(x)= {3x-4, 3 less than x use algebra to find each of the following limits: lim f(x)= x→3^+ lim...

Find the absolute maximum and absolute minimum values of the function f(x)=x^3−12x^2−27x+10 over each of the indicated intervals. a) Interval [-2,0] 1. Absolute max= 2...

g(x)=∫ (x on top, 0 on bottom) √(1+6t) dt, use fundamental theorem of calculus find g1(x) (derivative of g(x). )

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 _________

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

The limit lim x→1 x^7−1/x−1 represents the derivative of some function f(x) at some number a. Find f and a. f(x)=_____ a=______

Determine the linear Lagrange interpolating polynomial that passes through the points (2,4) and (5,1). Please explain all steps so I can understand how you got your answer.

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

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