If lim_(x rarr-6)f(x)=9 and lim_(x rarr-6)k(x)=10, what is the value of lim_(x rarr-6)[k(x)-f(x)] ?

Given Limits: We are given the limits of two functions as x approaches -6: lim_(x -> -6)f(x) = 9 lim_(x -> -6)k(x) = 10 We need to find the limit of the difference of these two functions as x approaches -6.Properties of Limits: According to the properties of limits, the limit of the difference of two functions is equal to the difference of their limits, provided that both limits exist and are finite. So, we can write: lim_(x -> -6)[k(x) - f(x)] = lim_(x -> -6)k(x) - lim_(x -> -6)f(x)Substitute and Solve: Substitute the given limit values into the equation: lim_(x -> -6)[k(x) - f(x)] = 10 - 9Perform Subtraction: Perform the subtraction to find the limit of the difference: lim_(x -> -6)[k(x) - f(x)] = 1

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Q. If

\lim_{x \to -6}f(x)=9

and

\lim_{x \to -6}k(x)=10

, what is the value of

\lim_{x \to -6}[k(x)-f(x)]

Given Limits: We are given the limits of two functions as $x$ approaches $-6$ :
$\lim_{x \to -6}f(x) = 9$
$\lim_{x \to -6}k(x) = 10$
We need to find the limit of the difference of these two functions as $x$ approaches $-6$ .
Properties of Limits: According to the properties of limits, the limit of the difference of two functions is equal to the difference of their limits, provided that both limits exist and are finite. $\newline$ So, we can write: $\newline$ $\lim_{x \to -6}[k(x) - f(x)] = \lim_{x \to -6}k(x) - \lim_{x \to -6}f(x)$
Substitute and Solve: Substitute the given limit values into the equation: $\lim_{x \to -6}[k(x) - f(x)] = 10 - 9$
Perform Subtraction: Perform the subtraction to find the limit of the difference: $\newline$ $\lim_{x \to -6}[k(x) - f(x)] = 1$