1. Given the function y = , answer the following questions: (a) Use the limit definition to find the slope of the tangent to the curve at the point (1, 2).

Q: if the tangent line to y=F(x) at (4,3) passes through the point (0,2), find f(4) and f'(4).

A: Concept - use the slope formula of straight line

Q: 1. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = 5 – x² AT (3,–4).

A: f(x)=5-x2 To find the slope of tangent, we can use two alternatives (1) Direct derivative (2)…

Q: Given that the graph of f(x) passes through the point (2, 2) and that the slope of its tangent line…

A: Solution:

Q: For the following function, make a table of slopes of secant lines and make a conjecture about the…

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Q: If the slope of the tangent line to the graph of y=f(x) at x=a is m(a)=2a+1, and fl-1)=2, then what…

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Q: What is the slope of the tangent line that touches the graph of In(y) +e-=3y– 4x at the point A В) з…

A: slope , m=dydx.

Q: Given that the graph of f(x) passes through the point (3, 10) and that the slope of its tangent line…

A: Consider the given slope of tangent of the function at x,fx is 2x+6

Q: If the tangent line to y=f(x) at (4,3) passes through the point ( 0,2) , find f(4) ,f  '(4)

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Q: Given that the graph of f(x) passes through the point (8,8) and that the slope of its tangent line…

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Q: If y = Vr² + e(1-2), the slope of the tangent line to the graph of y at a = 0is

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Q: For the following function, make a table of slopes of secant lines and make a conjecture about the…

A: To Determine: For the following function, make a table of slopes of secant lines and make a…

Q: If the tangent line to y= f(x) at (4, 3) passes through thepoint (0, 2), find  f(4 )and f'(4)

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Q: Use the limit definition to find the slope of the tangent line to the graph off at the given point.…

A: Given that ,  f(x) = 9x+9  at the point   (1,18) To find the slope of the tangent line to the graph…

Q: Find the slope mm of the tangent line to the curve f(x)=x^3 at the point (1, 1) by using the…

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Q: Let f=sqrt(4x+3) and find the values below  1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x)/ h)…

A: Consider the given function

Q: Given that the graph of f(x) passes through the point (4, 3) and that the slope of its tangent line…

A: topic - functions

Q: Given: f(x)=x2+2 find the equation of a line tangent at point P(1,3) using limits

A: To find the equation of a line tangent at point P(1,3) on below curve using limits.

Q: What is the slope of the tangent line that touches the graph of In(y) +e-'=3y – 4x at the point.12

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Q: If y = f(x), f'(x), (f(x+h)-f(x)) and slope of the tangent to the curve of f(x), h lim h→0 they all…

A: if y = f(x) Then,  By first principle of derivative

Q: Given that f(2)=−3 and f′(2)=6, find an equation for the tangent line to the graph of y=f(x) at x=2.

A: For the function y=f(x), slope of the tangent at any point (a, f(a)) is given by mT=f'(x) at (a,…

Q: Given that the graph of f(x) passes through the point (7, 6) and that the slope of its tangent line…

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Q: What is the slope of the tangent line that touches the graph of In y + e2z-1 = 3y – 4x at the point…

A: Given that: lny+e2x-1=y-4x

Q: If the slope of the tangent line to the graph of y-f(x) at x=a is m(a)=2a+1, and f(1)=5, then what…

A: m(a)= 2 a + 1 f'(x) = m(x) = 2x +1  Integrating f'(x) gives f(x); f(x) = 2(x2/2) + x + c f(x) = x2 +…

Q: If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4). f(4)…

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Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A: As per instructions we solve it by limit definitely of derivative .

Q: 3. Given that the graph of f passes through the point (2,5) and that the slope of the tangent line…

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Q: The slope of the tangent line is the limit of the slopes of the secant lines. Thus, to estimate the…

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Q: If the tangent line to y = f(x) at (4, 2) passes through the point (0, 1), find f(4) and f'(4). f(4)…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: For the following function, make a table of slopes of secant lines and make a conjecture about the…

A: To evaluate slopes of secant lines in the neighbourhood of x = pi/2 and estimate the slope of the…

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(z) =…

A:

Q: 8) Based on the graph of y = g(t) below, state the value of each limit if it exists. If it does not…

A: Observing from the given graph we have

Q: Given that the graph of f(x) passes through the point (5,10)( and that the slope of its tangent line…

A: Given , The graph of f(x) passes through the point (5,10) and that the slope of its tangent line at…

Q: Find f(x) if f(1) 7 1 and the tangent line at (x, f(x)) has slope f(x) =

A: We know that the slope of tangent at any point to the curve of a function is given by the derivative…

Q: Given that the graph of f(x) passes through the point (4, 2) and that the slope of its tangent line…

A: Recall: The slope of the tangent line to the curve f(x) is f'(x).

Q: Given that the graph of f(x) passes through the point (3, 2) and that the slope of its tangent line…

A: Given: Graph of f(x) passes through the point (3,2) and that the slope of its tangent at (x,f(x)) is…

Q: If the tangent line to y = f(x) at (5, 2) passes through the point (0, 1), find f(5) and f'(5). f(5)…

A: Topic = Derivative f5=2f'5=15

Q: slope

A:

Q: Given that the graph of f(x)  passes through the point (4,10) and that the slope of its tangent line…

A: Given that the graph of f(x)  passes through the point (4,10) and that the slope of its tangent line…

Q: Find an equation of the tangent line to the graph of the function                    y = esinh x, at…

A: Slope of the tangent line is the derivative of the given curve at the given point. So…

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A:

Q: Given the function, Show that it is not continuous at (3,-1) and determine the slope of the line…

A: The function will be discontinuous at 3, -1, if  either f(3,-1) is not defined, or,…

Q: Suppose the curve y=f(x) has a tangent line y=4x-5 at x=1. Consider the function g(x)=2f(x)+x+1 What…

A: equation of tangent is y=4x-5 therefore equation of curve whose tangent is y=4x-5 ,…

Q: Given that the graph of f(x) passes through the point (10, 8) and that the slope of its tangent line…

A: Solution )slop of tangent line                f'(x) = 2x + 5 Intregating both sides  ∫f'(x) =…

Q: Given that the graph of f(x) passes through the point (5,10) and that the slope of its tangent line…

A: The graph of f(x) passes through the point (5,10) and that the slope of its tangent line at (x,f(x))…

Q: Given that f(−5)=−10 and f′(−5)=−2, find an equation for the tangent line to the graph of y=f(x)at…

A: Topic = Functions

Q: If the tangent line to the curve y= f(x) at (5 , 20) is y = 6x – 10, then limh→0- f(5+h)–f(5) h…

A: For a function f the derivative at x=a is defined as f'(a)=limh→0f(a+h)-f(a)h. Tangent line to a…

Q: Given that the graph of f(x) passes through the point (2, 4) and that the slope of its tangent line…

A: Explanation of the answer is as follows

Q: Given that the graph of f(x) passes through the point (8, 2) and that the slope of its tangent line…

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Q: 5 7. Find the slope of the tangent line to the graph of y = x² at the point where x = –

A: