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Pebbles are poured out of a tube at one cubic meter per second. It forms a pile which has the shape of a cone. The height of the cone is equal to the radius of circular base. How fast is the pile of pebbles rising when it is 2 meters high
A car manufacturing company was able to release 1,860 units at the end of January. Based on records, they were able to increase their sales by 46 units per month thereafter. In what month did their car sales reach 2, 320 units?
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.)
