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Calculus

1. A certain radioactive element has a half-life of 5 hours. If its initial mass is at

6,470 grams, how many grams are left after 2 days?

2. Carlo’s online investment is worth Php870,000 on its 3rd year and Php650, 000

on its 7th year. What is the worth of his initial investment?

3. The pressure exerted on us by the atmosphere decreases exponentially as you

go up. The pressure at ground level is 1,013 hPa and decreases to 965 hPa at

381 meters. What is the pressure at the summit of Mt. Apo which is at 2,954

meters?

4. A strain of bacteria growing on the palm of your hands is 9 bacteria after 6

minutes. If you start with only one bacterium and follows an exponential growth

model, how many bacteria could be present at the end of 1 hour?

5. A certain breed of rats doubles its population every 2 months. Assuming there

were only 6 rats initially at a certain area, how many months will it take for the

population to grow to 68 rats?

Calculus

Compute the area of the plane region bounded by the curve x=y^{2}-2 and the line y=-x using integration along the y-axis.

Calculus

Consider the R²-R function defined by f(x,y)=x²-2x-y and let c be the contour curve of f at level 0.

1.find a Cartesian equation for the tangent line L to C at the point (-1,3).

2.sketch the contour curve C together with the line L in R².show all intersections with the axes.

3.find an equation for the tangent plane V to the graph of f in R³ at the point (-1,3,0).

Calculus

A delivery company needs the measurements of a rectangular box such that the length plus twice the width plus twice the heights should not exceed 150cm.what is the maximum volume of such a box?

Calculus

Consider the R²-R function f defined by f(x,y)=x²+2y²-x²y.

Show that f has two saddle points

Calculus

Consider the R²-R function f defined by f(x,y)=e^xIn(1+y).

Find the third order Taylor polynomial of f about the point (0,0)

Calculus

Convert (√3,-1)into polar coordinates (r,0) so that r≥0 and 0≤0<2π

Calculus

Find implicit differentiation of 2y+cot(xy^2)=3xy

Calculus

A rock is thrown horizontally from the top of a cliff 88 m high, with a horizontal speed of 25 m/s. with what velocity does the rock hit

Calculus

Derive an equation *x*(*t*) for the instantaneous position of the car as a function of time. Identify the

● value *x* when *t* = 0 s

● asymptote of this function as *t* → ∞

**t(0-28 m/s) (s) t(400m)(s) t (Maxspeed)(s)**

** 2.5 9.75 8.0**