This is calc!

1)A production formula for a student's performance on a difficult English examination is given byg(t,x) =4tx0.1t²x²,

wheregis the grade the student can expect to get,tis the number of hours of study for the examination, andxis the student's grade-point average.(a) Calculate g_t(10, 3)and g_x(10, 3).

gt(10, 3)	=
gx(10, 3)	=

Interpret the results. If you have studied forhours and have a GPA of, your score on the examination is increasing bypoints for each additional hour of study and bypoints for each additional point of GPA. (b) What does the ratio

g_t(10, 3)

g_x(10, 3)

tell about the relative merits of study and grade-point average? At a level ofhours of study with a GPA of, one additional hour of study is equivalent to an increase of(rounded to three decimal places) in GPA (as far as your test score is concerned).

2)

Find

f

x

,

f

y

, and

f

z

.HINT [See Example 3.] f(x,y,z) =

26

x²+y²+z²

f x	=
f y	=
f z	=

Find their values at (0,1, 1) if possible. (If an answer is undefined, enter UNDEFINED.)

f x (0,1, 1)	=
f y (0,1, 1)	=
f z (0,1, 1)	=

3)

Find

f

x

,

f

y

, and

f

z

.HINT [See Example 3.] f(x,y,z) =

e^0.1x

1 +e^0.6y

f x	=
f y	=
f z	=

Find their values at (0,1, 1) if possible. (If an answer is undefined, enter UNDEFINED.)

f x (0,1, 1)	=
f y (0,1, 1)	=
f z (0,1, 1)	=