Calculus Answers

State whether the following statements are true or false. Give reasons for your answers
(1) The function f:R^3®R, given by f( x, y, z) =|x|+|y|+|z| is differential at (2, 3,-1).
(2) The function f(x, y) =max{y/x, x} is a homogenous function on R^2.
(3) The domain of the f/g where f(x, y) =2xy and g(x, y) =x^2+y^2 is R^2.

Find the two repeated limits of the function f(x,y)=(y-x/y+x)(1+x^2/1+y^2) at (0,0).Does the simultaneous limit of f exist as (x,y) to (0,0)?Give reasons for your answer

check whether the limit of the function f (x,y)=3x^3y/x^6+2y ^2 exists as (x,y) to(0,0)

For all even integral values of n , lim
x-infinite (X+1)^-n exists

A certain radioactive isotope has a half-life of 15 days. If one is to make a table showing the half-life decay of a sample of this isotope from 32 grams to 1 gram; list the time (in days, starting with t=0) in the first column and the mass remaining (in grams) in the second column, which type of sequence is used in the first column and which type of sequence is used in the second column?

Integrate ∫x^2+x+5/(x^2+4)(x+1)dx

Integrate ∫(3x+1)sqrt (4x^2+12x+5)dx

Find the intervals on which the function f defined by f( x )=x⁴-8x²+16is concave upward or concave downward.

Given data is that car has a model that states use equation (7 at top 0 and bottom of integral) 7^0∫v(t)dt, 0-28m/s of 2.6s, time of reach 400m of 10.46s and tmaxspeed of 7s. I have calculated that value of coefficient A is 90.25m/s and time to reach max acceleration is 23.7m/s². I'm certain that the max velocity is at t=7 v(7)=90.25 x (1-e^-10 = 57.05m/s). Please draw a graph for velocity v time showing velocity m/s on y axis also labelled with A, max velocity/speed. Then on the x axis please show where tmax is hit and where t400 is hit with x axis labelled time (s) please also show Vmax along the graph. once this is done please work out the areas for both sections and write a brief explanatation on the comparison between the model and my results :)

Given data is that car has a model that states use equation (7 at top 0 and bottom of integral) 7^0∫v(t)dt, 0-28m/s of 2.6s, time of reach 400m of 10.46s and tmaxspeed of 7s. I have calculated that value of coefficient A is 90.25m/s and time to reach max acceleration is 12.9m/s². I'm certain that the maximum velocity is V(t → ∞) = 90.25m/s. Please draw a graph for velocity v time showing velocity m/s on y axis also labelled with A, max velocity/speed. Then on the x axis please show where tmax is hit and where t400 is hit with x axis labelled time (s) please also show Vmax along the graph. once this is done please work out the areas for both sections and write a brief explanatation on the comparison between the model and my results :)