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- https://math.libretexts.org/Courses/Butler_Community_College/MA148%3A_Calculus_with_Applications_-_Butler_CC/02%3A_The_Derivative/2.01%3A_Prelude_to_the_DerivativeThe slope of a line measures how fast a line rises or falls as we move from left to right along the line. The answer, as suggested in the figure, is to find the slope of the tangent line to the curve ...The slope of a line measures how fast a line rises or falls as we move from left to right along the line. The answer, as suggested in the figure, is to find the slope of the tangent line to the curve at that point. As you may be able to see in the image below, the closer the point \(Q\) is to the point \(P\), the closer the secant slope gets to the tangent slope.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2160%3A_Applied_Calculus_I/01%3A_The_Derivative/1.01%3A_Prelude_to_the_DerivativeThe slope of a line measures how fast a line rises or falls as we move from left to right along the line. The answer, as suggested in the figure, is to find the slope of the tangent line to the curve ...The slope of a line measures how fast a line rises or falls as we move from left to right along the line. The answer, as suggested in the figure, is to find the slope of the tangent line to the curve at that point. As you may be able to see in the image below, the closer the point \(Q\) is to the point \(P\), the closer the secant slope gets to the tangent slope.
- https://math.libretexts.org/Courses/Chabot_College/MTH_15%3A_Applied_Calculus_I/02%3A_Limits/2.04%3A_ContinuityWe can also conclude from the information in the table that \(f\) is not continuous at 2 or 3 or 4, because \( \lim\limits_{x\to 2} f(x) \neq f(2) \), \( \lim\limits_{x\to 3} f(x) \neq f(3) \), and \(...We can also conclude from the information in the table that \(f\) is not continuous at 2 or 3 or 4, because \( \lim\limits_{x\to 2} f(x) \neq f(2) \), \( \lim\limits_{x\to 3} f(x) \neq f(3) \), and \( \lim\limits_{x\to 4} f(x) \neq f(4) \). It is not defined at \(x = -3\), but we are taking the limit as \(x\) approaches 2, and the function is defined at that point, so we can use direct substitution:\[ \lim\limits_{x\to 2} \dfrac{x-4}{x+3} = \dfrac{2-4}{2+3}= -\dfrac{2}{5}. \nonumber \]
- https://math.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/MATH_110%3A_Techniques_of_Calculus_I_(Gaydos)/02%3A_The_Derivative/2.00%3A_Prelude_to_the_DerivativeThe slope of a line measures how fast a line rises or falls as we move from left to right along the line. The answer, as suggested in the figure, is to find the slope of the tangent line to the curve ...The slope of a line measures how fast a line rises or falls as we move from left to right along the line. The answer, as suggested in the figure, is to find the slope of the tangent line to the curve at that point. As you may be able to see in the image below, the closer the point \(Q\) is to the point \(P\), the closer the secant slope gets to the tangent slope.
