Calculate the difference quotients for H(x)=3lnx+4H(x)=3ln⁡x+4 using h=0.1h=0.1, 0.010.01, and 0.0010.001. Use the results to approximate the slope of the tangent line to the graph of H(x)H(x) at the point (e,7)(e,7). If necessary, round the difference quotients to no less than six decimal places and round your final answer to two decimal places.

Q: Find the equation of the tangent line at the given value of x on the curve. y° +xy² -61=x+3y°; x:…

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Q: Section 2.4 Chain Rule Please show & explain all work, thank you.

A: Multiply both sides by x^2.

Q: Find the slope of the tangent line to the graph at the given point. (4 – x)y? = x³, (2, 2) Cissoid:…

A: Slope of tangent line =dydx(4-x)y2=x3differentiating w.r.t 'x'y2d(4-x)dx+(4-x)dy2dx =…

Q: 3. Determine the slope of the tangent line to the curve f(x) = at (2x + 1)2 x = 1 by using the…

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Q: 7. Use implicit differentiation to find the slope of the tangent line to the graph of x +y = 19 –…

A: Here we will find the slope of tangent line to the given graph,

Q: Find an equation of the tangent line to the curve y = 7tan(5x) at the point (0, 1)

A: According to Bartleby only first question can be solved at a time Please find the solution

Q: Find the slope of the tangent line to the curve - 2x2 + 3xy + ly 38 - at the point (1, – 3).

A: Given:   To determine: Slope of the tangent line to the given curve at point (1, -3)

Q: Find an equation of the tangent line to f(x) = 3x +5 at the point (1, 8).

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Q: 2. Use implicit differentiation to find an equation of the tangent line to the curve z2+2ry-y²+x = 2…

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Q: Find an equation of the tangent line to the curve at the given point. y = 5x/(x+4),    (1, 1)

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Q: Find the slope of the tangent line to the curve of y = x 2 at the point where x = −6

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

Q: 4. Find the equation of the tangent line to the function y= In(x* -2) when x=3.

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Q: Find the equation of the tangent line to f(x) =1 – x² at (1,0). -

A: here we use formula  y-y1=m(x-x1) at point (1,0)

Q: The slope of the tangent line to the graph of x2 – y? = ln(xy) at the point (1, 1) is

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Q: Find the equation of the tangent line to the curve 3x f (x): at the point (1,). 1+5x2

A: Given: The function fx=3x1+5x2 and the point 1,12, To determine: The equation of tangent line to the…

Q: Find an equation of the tangent line to f(x) = x² at the point (3,9).

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Q: Find the slope of the tangent line to the curve defined by 4x + xy – y* 1760 at the point (8, –4). e…

A: To find the slope of the tangent line to the given curve at the given point

Q: Where on the interval [0, 4] does ƒ(x) = 4x - x2 have a horizontal tangent line?

A: Determine the value for derivative of f(x) i.e f'(x). fx=4x−x2f'x=ddx4x−x2=ddx4x−ddxx2=4×ddxx−2xSo,…

Q: Find the slope of the tangent line to the graph at the given point.

A: Slope:  The slope of a line measures the steepness of the line. The slope is calculated by rise over…

Q: Find f(x) if f(1) = -1 and the tangent line at (x, f(x)) has slope 3ex+7 f(x)= ?

A: Given:

Q: Find the slope of the tangent line to the curve y3 + yx2 + x2 − 3y2 = 0 at the point P(0, 3) by…

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Q: Find the equation of the tangent line to the curve x4+y4=2 at the point (1,1)

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Q: The slope of the tangent line to the curve x^3 + y^3 = 6xy at the point (3,3) is

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Q: Find an equation of the tangent line to f(x)=-x – 4x at the point (-1,5).

A: The above question is answered in next step and we can find the equation of the tangent line

Q: Find the equation of the tangent line to y = 2r5 - 3x³ at the point where x = 0.7, with coefficients…

A: Methods to find the equation of the tangent at a point helps to find the required answer to the…

Q: Find an equation of the tangent line to the graph of the function at the given point. y = 4 – x² –…

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Q: Find the slope of the tangent line at the indicated point * y = Vx2 – 2x at x = 3

A: Here, y=x2-2x So, the slope of the tangent at x=3 is: dydxx=3

Q: Find the slope of the tangent line to the curve - 2x2 + 2xy – 4y³ = 0 at the point (1, – 1). -

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Q: 7. Use implicit differentiation to find the slope of the tangent line to the curve 3(28x + y)/2 = 5y…

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Q: Find an equation of the tangent line to the graph of the function                   y=2x2 + ln x2 ,…

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Q: Find the slope of the tangent to the curve y2 ln(x) + x2y = 7 at (1, 7)

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Q: Find the tangent line to the curve y = 2x - x2 at (2,0)

A: The equation of the curve is given by y = 2x-x2 The point is x0, y0 = 2, 0 Formula Used: The formula…

Q: Find the slope of the tangent line to the curve y = arctan(13x +e) at the point (0, 7/2).

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = 4 – x² –…

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Q: Find the equation of the tangent line (in point-slope form) to . 2 f(x) = 3 – 2x' + In(5x + e) at x…

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Q: 2 Determine the equation of the tangent line to the graph of f(x) = Vx-12x at the point where x -3.

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Q: . Find the slope of the tangent line at the point P of (x² + y² )° = 4xy; P(1,1).

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Q: Find an equation of the tangent line to the graph of x° + 3xy² + y = 15 at the point (1, 2). y=

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Q: find the equation of the tangent line to the curve y=x 'square root of' x at the point (1,1).

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Q: Find the equation of the tangent line at the given point on the curve. x3 + 2xy – y2 = 11 at (2,3)

A: We need to find the equation of the tangent line at the given point on the curve. We have x3+2xy-y2…

Q: Find an equation of the tangent line to the graph of the function (x)= Vx –7 at the point (23, 4).

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Q: Find the slope of the tangent to the curve y² In(x) + x<y = 5 at (1, 5).

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Q: Find the slope of the tangent line to the curve 1x² − 2xy + 1y³ = 13 at the point (4,3).

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Q: Find the tangent line to y = √(x2 - x + 7) at x = 2.

A: Differentiating with respect to x, we get

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A: Given: 5x+2xy+4y2=25

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A:

Q: Find the equation of the tangent line to the graph of x2y2+4xy = 0 at the point (-4, 1).

A: Given: x2y2+4xy=0  at point -4,1

Q: Find an equation of the tangent line to the curve at the given point. f(x) = 7x2 - x³, (1, 6) y =

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Q: Find the x-coordinate of the point on the graph of y=x^2 where the tangent line is parallel to the…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: