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a spherical balloon is inflated at a rate of 36pi cm³/sec. How fast is the radius of the balloon increasing when radius is 7cm?

Evaluate


d^2r/dt^2 at t=0 when


r=(t3+2t)i−3e−2tj+2sin5tk


Find the derivative of the following

1.y= (2x²+6)⁵

2. y=(5x-1/2x+3)³
      

3.g(x)=3xe3x

4. y=ecosx



Find the derivative of the following functions (use the Rules of differentiation)


1.) y=(5x²-2x+1)²


2.) f(x)= cos (5x)


3. y=e exponent of 2x


4. g(x)= 10 exponent of x


find the general term of the sequence, starting with n = 1. Determine whether the sequence converges and if so find its limit. If the sequence diverges, indicate that using the checkbox.


3, 3/19, 3/19^2, 3/19^3...



Give an example of a function of two variables such thatf(0,0) = 0 butfis NOT continuousat (0,0). Explain why the functionfis NOT continuous at (0,0).


Q4. Suppose that a population yy grows according to the logistic model given by formula:


yy = LL

1 + AAee−kkkk .

a. At what rate is yy increasing at time tt = 0 ?

b. In words, describe how the rate of growth of yy varies with time.

c. At what time is the population growing most rapidly?


Given the function y=√x

a. Find the differential dy.

b. Evaluate dy and ∆y if x=1 and dx=∆x=1

c. Find the equation of the tangent line at x=1

d. Sketch the graph of the curve y=√x and the tangent line in the Cartesian Plane using a scale of 1 unit = 1cm. Show in your diagram the line segments dx, dy, and ∆y. (Note: the curve us an upper semi-parabola whose vertex is at the origin and concaving to the right. Use 0, 1, 4, and 9 as x-coordinates.)


Poiseuille’s law asserts that the speed of blood that is r centimeters from the central axis of an artery of radius R is S(r) = c(R^2 − r^2), where c is a positive constant. Where is the speed of the blood greatest?


Let E be the solid bounded by y = x^2, z = 0, y + 2z = 4. Express the integral