How do you find f'(x) using the limit definition given # f(x)= 2x^2x#?
Therefore,
Enjoy Maths.!
By signing up, you agree to our Terms of Service and Privacy Policy
To find (f'(x)) using the limit definition, where (f(x) = 2x^2  x), follow these steps:

Start with the limit definition of the derivative: (f'(x) = \lim_{h \to 0} \frac{f(x + h)  f(x)}{h}).

Substitute the given function (f(x)) into the limit definition: (f'(x) = \lim_{h \to 0} \frac{2(x + h)^2  (x + h)  (2x^2  x)}{h}).

Expand and simplify the numerator: (f'(x) = \lim_{h \to 0} \frac{2(x^2 + 2hx + h^2)  x  h  2x^2 + x}{h}).

Combine like terms in the numerator: (f'(x) = \lim_{h \to 0} \frac{2x^2 + 4hx + 2h^2  x  h  2x^2 + x}{h}).

Simplify the expression in the numerator: (f'(x) = \lim_{h \to 0} \frac{4hx + 2h^2  h}{h}).

Factor out (h) from the numerator: (f'(x) = \lim_{h \to 0} \frac{h(4x + 2h  1)}{h}).

Cancel out the (h) terms: (f'(x) = \lim_{h \to 0} (4x + 2h  1)).

Substitute (h = 0) into the expression: (f'(x) = 4x  1).
So, (f'(x) = 4x  1).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 Using the limit definition, how do you find the derivative of #f(x)=4x^2 1#?
 What is the equation of the line tangent to # f(x)=x/(x^24) # at # x=1 #?
 How do you find the equations for the normal line to #x^2+y^2=20# through (2,4)?
 What is the instantaneous velocity of an object moving in accordance to # f(t)= (t^2,e^tt^2) # at # t=3 #?
 How do you find the slope of the tangent line to the graph of #f(x)=x^2/(x+1)# at (2, 4/3)?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7