A function of three variables is given by, f (x,y,t) = x3y2sin t + 4x2t + 5yt2 + 4xycos t Find ft (3.44,0.58,8.1) giving your answer to 3 decimal places.
anybody please help me... thanks a million... got stuck with this qns..
I am not certain what your ft means.
f((3.44,0.58,8.1)= ans obtained by putting in x,y, t into the equation. This is not a calculator friendly punch in, paste this in your google search window
(3.44^3)*((0.58)^2)*sin (8.1) + 4*(3.44)^2*(8.1) + 5(0.58)(8.1)^2 + 4*(3.44)*(0.58)*cos(8.1=
CHECK IT. The only issues I question what units is t in? radians, degrees, or what?
It just occured to me, you might have meant ft the partial derivative of f with respect to t. That is not what is above.
ft = f(t)
t should be in radians mode..
f(t) is meaningless since f is a function of (x,y,t). If you want
∂f/∂t then that just think of x and y as constants:
f(x,y,t) = x^3 y^2 sin t + 4x^2 t + 5yt^2 + 4xycos t
∂f/∂t = x^3 y^2 cos t + 4x^2 + 10yt - 4xy sin t
(3.44,0.58,8.1)
= 3.44^2*0.58^2 cos(8.1) + 4*3.44^2 + 10*0.58*8.1 - 4*3.44*0.58*sin(8.1)
= 97.131
To find ft (3.44, 0.58, 8.1), we need to find the partial derivative of the given function f(x, y, t) with respect to t, holding the other variables (x and y) constant.
The given function is:
f(x, y, t) = x^3 * y^2 * sin(t) + 4 * x^2 * t + 5 * y * t^2 + 4 * x * y * cos(t)
To find ft (the partial derivative of f with respect to t), we differentiate each term in f with respect to t while treating x and y as constants.
Differentiating the first term:
d/dt (x^3 * y^2 * sin(t)) = x^3 * y^2 * cos(t)
Differentiating the second term:
d/dt (4 * x^2 * t) = 4 * x^2
Differentiating the third term:
d/dt (5 * y * t^2) = 10 * y * t
Differentiating the fourth term:
d/dt (4 * x * y * cos(t)) = -4 * x * y * sin(t)
Now, summing up all the differentiated terms, we get:
ft(x, y, t) = x^3 * y^2 * cos(t) + 4 * x^2 + 10 * y * t - 4 * x * y * sin(t)
To find ft(3.44, 0.58, 8.1), substitute the given values into the expression for ft:
ft(3.44, 0.58, 8.1) = (3.44^3) * (0.58^2) * cos(8.1) + 4 * (3.44^2) + 10 * 0.58 * 8.1 - 4 * 3.44 * 0.58 * sin(8.1)
Calculating the expression gives us the value of ft(3.44, 0.58, 8.1).
Note: Remember to use a calculator or a computer program to evaluate the expression accurately and round the final answer to 3 decimal places as required.