Let f(x)=1/x. Compute the difference quotient for f(x) at x=1 with h=0.3
I know that the formula for difference quotient is (f(x+h)-f(x))/h, but I am not sure how I am supposed to plug this in. I have tried a few ways but webworks says that the answer is wrong every time.
Well, it seems like you're having a "h-ing" trouble with this one. Don't worry, I'm here to help you clown around with it!
To find the difference quotient for f(x)=1/x, we need to plug in x=1 and h=0.3 into the formula. Let's give it a shot:
Step 1: Plug in f(x+h)
f(1+0.3) = f(1.3) = 1/(1.3)
Step 2: Plug in f(x)
f(1) = 1/1 = 1
Step 3: Subtract the two and divide by h
(1/(1.3) - 1) / 0.3
Now, let's simplify that expression a bit:
Step 4: Finding a common denominator to subtract the fractions.
(1/(1.3) - (1 * 1.3)/(1.3)) / 0.3
(1/(1.3) - 1.3/1.3) / 0.3
(1/(1.3) - 1.3/1.3) / 0.3
((1 - 1.3)/(1.3)) / 0.3
Step 5: Simplify the numerator and divide by h
(-0.3/1.3) / 0.3
(-0.3/1.3) * (1/0.3)
-0.3/(1.3*0.3)
-0.3/0.39
And there you have it! The difference quotient for f(x)=1/x at x=1 with h=0.3 is approximately equal to -0.769.
Remember to keep practicing, and soon you'll be "h"ilariously good at these math problems!
To compute the difference quotient for f(x) at x=1 with h=0.3, we need to plug in the values into the given formula:
The formula for the difference quotient is:
(f(x+h) - f(x)) / h.
Let's calculate f(x+h) and f(x) first.
f(x+h) = 1 / (x+h)
f(1+0.3) = 1 / (1+0.3) = 1 / 1.3
f(x) = 1 / x
f(1) = 1 / 1 = 1
We can now substitute these values into the difference quotient formula:
[(1 / 1.3) - 1] / 0.3
Simplifying further:
[1 - 1.3] / 1.3 * 0.3 = (-0.3) / 1.3 * 0.3
Finally, we get:
-0.3 / 1.3 * 0.3 = -0.915
Therefore, the difference quotient for f(x) at x=1 with h=0.3 is -0.915.
To compute the difference quotient for f(x) at x=1 with h=0.3, you need to follow these steps:
Step 1: Determine f(x+h)
To find f(x+h), substitute x+h into the function f(x):
f(x+h) = 1 / (x+h)
Step 2: Determine f(x)
To find f(x), substitute x into the function f(x):
f(x) = 1 / x
Step 3: Calculate the difference quotient
Substitute the values obtained from steps 1 and 2 into the formula for the difference quotient:
[f(x+h) - f(x)] / h = [1 / (x+h) - 1 / x] / h
At this point, it may seem tricky to simplify or evaluate further since the expression contains fractions. However, we can simplify it by finding a common denominator.
Step 4: Finding a common denominator
To find a common denominator, multiply the first fraction by (x / x) and the second fraction by ((x+h) / (x+h)):
[(1 / (x+h)) * (x / x) - (1 / x) * ((x+h) / (x+h))] / h
Step 5: Simplify the numerator
Simplify the numerator by multiplying out and combining like terms:
[(x - (x + h)) / (x(x+h))] / h
Step 6: Simplify the numerator further
By distributing the negative sign inside the parentheses and simplifying, we get:
(-h / (x(x+h))) / h
Step 7: Simplify the expression
The h terms in the numerator and denominator cancel out:
-1 / (x(x+h))
Therefore, the difference quotient for f(x) at x=1 with h=0.3 is -1 / (x(x+h)), which can also be simplified as -1 / (x(x+0.3)).
Remember to double-check your calculations or use a calculator to evaluate the equation with specific values for x and h.
just do what it says ...
f(x+h) , if h = .3
= f(x+.3) = 1/(x+.3)
so (f(x+h)-f(x))/h
= (1/(x+.3) - 1/x)/.3
= ((x - x - .3)/(x(x+.3))/.3
= ( -.3/(x(x-.3) )/.3
= -1/(x(x+.3))