The value of the expression will be 10x – 3. Then the correct option is C.
What is the limit?
The value that approaches the output for the given input value. Limits are a very important tool in calculus.
The function is defined as,
f(x) = 5x² – 3x + 2
Then the value of the expression will be
[tex]\rightarrow \displaystyle \lim_{h \to 0} \dfrac{f(x+h)-f(x)}{h}[/tex]
Substitute the value of the function, then the value of the expression will be
[tex]\rightarrow \displaystyle \lim_{h \to 0} \dfrac{5(x+h)^2 - 3(x + h) + 3- 5x^2 + 3x - 3}{h}\\\\\\\rightarrow \displaystyle \lim_{h \to 0} \dfrac{5x^2 + 5h^2 + 10xh - 3x - 3h + 3- 5x^2 + 3x - 3}{h}\\\\\\\rightarrow \displaystyle \lim_{h \to 0} \dfrac{ 5h^2 + 10xh - 3h }{h}\\[/tex]
Simplify the equation further, then we have
[tex]\rightarrow \displaystyle \lim_{h \to 0} 5h + 10x - 3 \\[/tex]
Substitute the value of the h = 0, then the value of the expression will be
⇒ 5(0) + 10x – 3
⇒ 10x – 3
Then the correct option is C.
More about the limit link is given below.
https://brainly.com/question/8533149
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