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Calculus
Is there a number 'a' such that lim┬(x→-2)〖(3x^2+ax+a+3)/(x^2+x-2)〗exists? For such 'a' (if any), find lim┬(x→-2)〖(3x^2+ax+a+3)/(x^2+x-2)〗.
Calculus
The slope of the tangent line to the graph of the function y=4x^3 at the point (3,108) is lim x↦3 (4x^3−108)/(x−3). By trying values of x near 3, find the slope of the tangent line.
Calculus
Let f={4−x^2 if x≤2
{x-1 if x>2
Find each of the following limits.
(a) limx→2^- f(x)
(b) limx→2^+ f(x)
(c) limx→2f f(x)
{x-1 if x>2
Find each of the following limits.
(a) limx→2^- f(x)
(b) limx→2^+ f(x)
(c) limx→2f f(x)
Calculus
Let b > 0 and b≠1. We consider the function f(x) = b^x with domain D = lR. Determine the inverse function f^-1(y) write it in terms of the natural logarithm ln y, and specify its domain. What happens if b = 1?
Calculus
find the radius of curvature at point (s,psi)of the curve s=a log tan (pi/4+psi/4).
Calculus
Give an example of incomplete field that may be ordered.
Calculus
The gas substance consist of nitrogen oxide and oxygen. Find the oxygen concentration when nitrogen oxide oxides with maximal rate.
Calculus
Justify, with a written explanation or a mathematical reasoning and with a sketch of at least two different cases,
the following properties of integrals:
a) If f(x) is less than or equal to g(x) for a<=x<=b then
integrate from a to b of f(x)dx is less than or equal to integrate from a to b of g(x)dx
b)abs(integrate from a to b of f(x)dx) is less than or equal to integrate from a to b of abs(f(x))dx
the following properties of integrals:
a) If f(x) is less than or equal to g(x) for a<=x<=b then
integrate from a to b of f(x)dx is less than or equal to integrate from a to b of g(x)dx
b)abs(integrate from a to b of f(x)dx) is less than or equal to integrate from a to b of abs(f(x))dx
Calculus
ln 0.233 =(-1.455) but how?
Calculus
Solve for x and perform the functions.
log3 (2^x) = 10
Mod(Ceil(x), 3) ‐‐‐ this is a nested function call, ceil is executed first, then mod.
log3 (2^x) = 10
Mod(Ceil(x), 3) ‐‐‐ this is a nested function call, ceil is executed first, then mod.
