Differentials
Calculate the differential (dy)of
y=e^(2x) +sin(x^2)
[2e^(2x) +2xcos(x^2)]dx
Use Linear approximation to estimate the value of ln(1.38)
0.38
Find the Quardric approximation of
f(x)=1/(1-x)
centered at x=0.
1+x+x^2
Find the derivative (with respect to x) of
f(x) = ((sqrt(pisin(e)+e^(1000)))+sin(pi^125))/(sum_1^100 pi^e +floor(e^1000)
0
Find the differential(dy) of
y=4sqrtx
when x changes from 4 to 4.3
0.3
Compute the value of
lim_(x->0) tan(5x)/(2x)
(Hint: replace tan(5x) with the linear approximation)
2.5
Find the quadratic approximation of the function f(x)=3sin(2x) at
x=-pi/4
-3+6(x+pi/4)^2
What -40 degrees Fahrenheit equals in Celsius?
-40 degrees Celsius
Use differentials to estimate the change in the volume of a sphere when the radius changes from 10 cm to 10.05 cm.
20pi cm^3
Evaluate the value of
lim_(x->7) (ln(x-6))/(1-e^(x-7)
(hint: replace both numerator and denominators with linear approximations)
-1
Compute the value of
lim_(x->0) (9x^2)/(1-cos(6x))
(Hint: replace the denominator with quaradic approximation)
0.5
What is the next number in this sequence: 0, 7, 26, 63, 124 …..?
215