calculus
posted by kale .
limit as delta x approaches 0 when f(x) = 4/ sqr x
Have to use the (F(x+delta x)f(x))/delta x method

just plug and chug
[f(x+h)f(x)]/h
4(x+h)^(1/2)  4*x^(1/2)
Now, to evaluate (x+h)^(1/2), use the binomial theorem:
(a+b)^n = a^n + n*a^(n1)*b^1 + n(n1)/2 * a^(n1)b^2 + ...
(x+h)^(1/2) = x^(1/2) + (1/2)*x^(3/2)*h + (1/2)(3/2)/2 * x^(5/2)h^2 + ...
(x+h)^(1/2)  x^(1/2) = (1/2)*x^(3/2)*h + (1/2)(3/2)/2 * x^(5/2)h^2 + ...
divide all that by h to get
(1/2)*X^(3/2) + (1/2)(3/2)/2 * x^(5/2)h + ...
= 1/2x^(3/2) + 3/8x^(5/2)*h + ...
As h>0, all the terms with h disappear, leaving just
1/2 x^(3/2)
multiply that by 4 from the original function, and you get
2x^3/2 = 2/√x^{3}
Respond to this Question
Similar Questions

math
Compute delta(y) and dy for the given values of x and dx=delta(x) y=x^2 , x=8 , delta(x)=0.5 Delta(y)= ? 
equibrium  help!
Consider the reaction CO(g) + H2O(g) <> CO2(g) + H2(g) Use the appropriate tables to calculate a) deltaG*f at 552*C b) K at 552*C I'm pretty sure I have a good idea of how to do this: I believe I can use GibbsHelmholtz equation … 
calculus
Find the following limit where f(x) = 4x2 − 3x. limit delta x > f(x + delta x) f(x)/delta x can someone please help me 
CALCULUS help please
Find the following limit where f(x) = 4x^2 − 3x. limit>(f(x+ delta x)f(x))/(delta x) delta x **delta x means the triangle symbol with x next to it*** 
Chemistry(Please check answers)
1) For a reaction delta Go is more negative than delta Ho. What does this mean? 
CalculusSolved  Incorrect
calculate delta y for f(x)= x^(3/2) with x= 4 and delta x= dx=0.1 delta y= f(x+delta x) f(x) = f(4.1)  f(4) delta y= f(4.1)8 f(x + delta x)= 8 + 3/2*x^(1/2)*0.1 = 8 + 0.15x^(1/2) = 8 + 0.30 = 8.30 delta y= 8.30  8 delta y= 0.30 … 
Chemistry
Please explain. The enthalpy changes for two different hydrogenation reactions of C2H2 are: C2H2+H2>C2H4 Delta H 1 C2H2+2H2>C2H6 Delta H 2 Which expression represents the enthalpy change for the reaction below? 
CHEMISTRY
Please explain. The enthalpy changes for two different hydrogenation reactions of C2H2 are: C2H2+H2>C2H4 Delta H 1 C2H2+2H2>C2H6 Delta H 2 Which expression represents the enthalpy change for the reaction below? 
Chemistry(DrBob222)
So, i did this lab, a solubility and thermodynamics lab of KNO3, and in it we had to determine the delta h delta g and delta s, the question i have is what is the relationship of the signs delta h, delta s, and delta g, to the dissociation … 
Calculus
I know the derivative of x is 1, but I'm having a hard time proving it with the limit definition of the derivative. I have... Lim delta x >0 (x+ delta x)(x)/delta x = 0 But I know the answer is 1. I don't understand what I am …