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The number a is real and such that the equation x^2 +2 (a - 1) x - a + 7 = 0 has
two different real negative solutions. One can then conclude that
(a) a <−2; (b) 3 <a <7; (c) it is impossible; (d) none of (a) - (c).
Consider the R 2 − R function f defined by
f(x,y) = (x^2+y)/y
Determine each of the following limits, if it exists.
a) lim f (x, y), where C1 is the curve y = x
(x,y)→C1 (0,0)
(b) lim f (x, y), where C2 is the curve y = 2x.
(x,y)→C2 (0,0)
(c) lim f (x, y), where C3 is the curve y = x 2
(x,y)→C3 (0,0)
(d) lim f (x, y).
(x,y)→(0,0)
Consider the R 2 − R function f defined by f(x,y) = x- 2y.
Prove from first principle that
lim f (x, y) = 0.
(x,y)→(2,1)
How fast is the surface area of a spherical balloon increasing when the radius is 10 cm and the volume is increasing at 15 cm3 /sec?
Find the sum of the infinite series ∑_(n=1)^(+∞)▒1/(k^2+5k+6)
Find the sum of the infinite series ∑_(n=1)^(+∞)▒2^(k+1)/3^(k+2)
Write out the first five-term of the sequence, determine whether the sequence converges, if so find its limit (i) {√(n^2+3n)-n}_(n=1)^(+∞) (ii) {((n+3)/(n+1))^n }_(n=1)^(+∞)
A 40-room hotel is fully occupied if Php 3000 is charged per day per room. For every 𝑥
hundred-peso increase in the daily rate, there are 𝑥 units vacant. What rate will maximize the
revenue of the hotel operation?
(i) Show that the sequence {n/(2n-1)}_(n=1)^∞ is monotonic. (ii) Is it bounded above and/or below? Give a reason for your answer. (iii) Can you concluded that it converges? Give a reason for your answer.
Find the equation of a curve in the xy-plane that passes through (1,3) and whose tangent at a point (x,y) has a slope (-6x(2+y))/√(〖3-3x〗^2 )
