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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
