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Question Number 158014 by zainaltanjung last updated on 30/Oct/21

$$ \\ $$$$ \\ $$

Answered by MathsFan last updated on 30/Oct/21

14

$$\mathrm{14} \\ $$

Commented by zainaltanjung last updated on 30/Oct/21

Okey

$$\mathrm{Okey} \\ $$

Commented by MathsFan last updated on 30/Oct/21

lim_(x→7) (((dy/dx)(x^2 )−(dy/dx)(49))/((dy/dx)(x)−(dy/dx)(7))) lim_(x→7) ((2x)/1) = 2(7) = 14

$$\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{7}} \frac{\frac{\mathrm{dy}}{\mathrm{dx}}\left(\mathrm{x}^{\mathrm{2}} \right)−\frac{\mathrm{dy}}{\mathrm{dx}}\left(\mathrm{49}\right)}{\frac{\mathrm{dy}}{\mathrm{dx}}\left(\mathrm{x}\right)−\frac{\mathrm{dy}}{\mathrm{dx}}\left(\mathrm{7}\right)} \\ $$$$\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{7}} \frac{\mathrm{2x}}{\mathrm{1}}\:\:=\:\mathrm{2}\left(\mathrm{7}\right)\:=\:\mathrm{14} \\ $$

Commented by zainaltanjung last updated on 31/Oct/21

Ok. you are right

$$\mathrm{Ok}.\:\mathrm{you}\:\mathrm{are}\:\mathrm{right} \\ $$

Answered by puissant last updated on 30/Oct/21

lim_(x→7) ((x^2 −49)/(x−7)) = lim_(x→7) (x+7)=14

$$\underset{{x}\rightarrow\mathrm{7}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} −\mathrm{49}}{{x}−\mathrm{7}}\:=\:\underset{{x}\rightarrow\mathrm{7}} {\mathrm{lim}}\left({x}+\mathrm{7}\right)=\mathrm{14} \\ $$

Commented by zainaltanjung last updated on 30/Oct/21

Okey. good

$$\mathrm{Okey}.\:\mathrm{good} \\ $$

Answered by Mr.D.N. last updated on 30/Oct/21

_(x→7) ^(lim) ((x^2 −49)/(x−7)) = _(x→7) ^(lim) ((x^2 −7^2 )/(x−7))= _(x→7) ^(lim) (((x+7)(x−7))/((x−7))) = _(x→7) ^(lim) (x+7) = 7+7=14//.

$$\:\underset{\mathrm{x}\rightarrow\mathrm{7}} {\overset{\mathrm{lim}} {\:}}\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{49}}{\mathrm{x}−\mathrm{7}} \\ $$$$\:=\underset{\mathrm{x}\rightarrow\mathrm{7}} {\overset{\mathrm{lim}} {\:}}\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }{\mathrm{x}−\mathrm{7}}=\underset{\mathrm{x}\rightarrow\mathrm{7}} {\overset{\mathrm{lim}} {\:}}\:\frac{\left(\mathrm{x}+\mathrm{7}\right)\left(\mathrm{x}−\mathrm{7}\right)}{\left(\mathrm{x}−\mathrm{7}\right)} \\ $$$$\:=\underset{\mathrm{x}\rightarrow\mathrm{7}} {\overset{\mathrm{lim}} {\:}}\left(\mathrm{x}+\mathrm{7}\right) \\ $$$$\:\:=\:\mathrm{7}+\mathrm{7}=\mathrm{14}//. \\ $$

Commented by zainaltanjung last updated on 31/Oct/21

Good.

$$\mathrm{Good}. \\ $$

Answered by mathlove last updated on 30/Oct/21

lim_(x→7) ((x^2 −49)/(x−7))=lim_(x→7) (((x−7)(x+7))/(x−7)) =lim_(x→7) x+7=14

$$\underset{{x}\rightarrow\mathrm{7}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} −\mathrm{49}}{{x}−\mathrm{7}}=\underset{{x}\rightarrow\mathrm{7}} {\mathrm{lim}}\frac{\left({x}−\mathrm{7}\right)\left({x}+\mathrm{7}\right)}{{x}−\mathrm{7}} \\ $$$$=\underset{{x}\rightarrow\mathrm{7}} {\mathrm{lim}}{x}+\mathrm{7}=\mathrm{14} \\ $$$$ \\ $$

Commented by zainaltanjung last updated on 31/Oct/21

Good

$$\mathrm{Good} \\ $$

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