Sketch the following function y = x² + 2x. a) Next, find the slope of the tangent line to the parabola at the point (-3, 3).- b) Construct the equation of that tangent line.

Q: Find the equation of the tangent line to the curve x' + y' = 6xy at (3,3). Write the equation in…

A: Given the curve x3+y3=6xy We need to find equation of the tangent line to the given curve at (3,3)…

Q: Find the equation of the tangent line at the given point on each curve. :x2 + y2 = 100; (8, -6)

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Q: Find the equation of the line tangent to the graph of f a

A: Given, f(x)=2+lnx4; x=e

Q: At the given point, find the equation of the tangent line, as requested. y^5+x^3=y^2+10x, tangent…

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Q: Write the equations of the lines tangent to the curve y x- 4x at both a 0 and a 2. Then, determine…

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Q: What are the coordinates of the points in the graph of y? – x² + 6x – 13 = 0 in which the tangent…

A: y2-x2+6x-13=0 --------------(1) Differentiating with respect to x ddxy2-x2+6x-13=ddx(0)…

Q: write an equation for the tangent line at the given point x +y = 4, (/2, V2)

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Q: Find an equation of the tangent line to the graph of the function at the point (9, 1). y = 2x - 9

A: Concept - used the formula of y-y1 =m(x-x1)  Here m=dy/dx=slope

Q: Find an equation of the tangent line to the curve at the given point.y=8x-6x^(2), P(4,-8)

A: y=8x-6x^(2), P(4,-8)Let the equation of the tangent: y=mx+cSlope of the tangent =m =  dy/dx.

Q: Find the equation of the tangent line of the given function at point (-1,3). Give answer in the…

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Q: Find the slope of the tangent line to the curve - 2.x? + 3xy + y – 118 - at the point (3, – 4).

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Q: Find the equation of the tangent line to y=−6/x^2 at x=−2. Write your answer in slope-intercept…

A: The equation of the curve is y = -6x2 To evaluate: The equation of the tangent line to the given…

Q: Write the equation of the tangent line to the graph of y = x2 at the point where x = 2.5.

A: To find the tangent line to a function at a given point first find the first derivative of the…

Q: Find the equation of the tangent to the curve r = θ when θ = π/2

A: Given problem:- Find the equation of the tangent to the curve r = θ when θ = π/2

Q: Find the slope and the equation of the tangent line to the curve and explain briefly.  y = 2x^2 –…

A: The slope of the curve at any point  x1,y1 can be calculated by using the formula m=dydxx1,y1 ,…

Q: Write the equation of the tangent line to the curve (a lemniscate) 2(x2 + y²)“ = 25(x² – y²) at the…

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Q: The equation of the tangent line to the curve 교+f -25, at (8,-12) is

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Q: Find the slope of the tangent line to the curve - l2? – 2æy – 2y³ = 19 at the point (3, - 2).

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Q: f(x) = 2x2 -4x +5 at the point (-1,11) %3D

A: fx=2x2-4x+5 find the derivative of fx with respect to x dfdx =ddx2x2-4x+5f'x=4x-4 Now we need to…

Q: Find an equation for a line that is tangent to the graph of y = ex andgoes through the origin.

A: To find the equation of a line that is tangent to the graph of y=ex and passing through origin.…

Q: Determine the equation of the line tangent to the graph given by y = at the point x +1 (4, }).

A: To find the equation of the line tangent to the graph y=xx+1 at the point 4,25

Q: Determine the equation of the tangent to y = (x – 7)(x+2) at the point P(-1,-8). Answer:

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Q: Determine the equation of the curve for which the tangent line at every point has a slope of 25, x =…

A: Topic = Coordinate geometry Correct option = D

Q: Determine the equation of the line tangent to the curve   at the point (-1,1) and reestablish a…

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Q: At what point on the curve x = 9t? + 9, y = 3 - 6 does the tangent line have slope

A: Given curves are And

Q: Give the equation of the tangent which passes through the point with the coordinate x=2 of the…

A: Equation of tangent problem.....

Q: Find the equation for the line tangent to the curve 2exy = x + y

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Q: at the indicated point, find the slope of the tangent to the curve c(x) = 3x^2 - 5 at (3, 22)

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Q: Find the equation of the tangent to the curve y=x²-x -2 at the point (1, -2).

A: We have to find the equation of the tangent to the curve y=x2-x-2 at the point (1,-2).

Q: Show At what points does the equation of the line tangent to the curve y=1/x+3 have a slope equal to…

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Q: Determine the equation of a tangent to the curve: y =. (x3 - 5x + 4)(3x2 - 2x) at the point (1,-2)

A: The given curve is y=x3-5x+43x2-2x at the point 1,-2.

Q: Find the equations of the tangent lines to the graph of x2(x2 +y?) = y2 when x =

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Q: (a) Use the definition of derivative to determine whether the parabola y = 2x2 – 13x + 5, have a…

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Q: Consider the following equation and point. f(x) = 3x2 – 6, (-1, -3) Find an equation of the tangent…

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Q: If f(x) = 8x2 - x3, find f'(2) and use it to find an equation of the tangent line to the curve y =…

A: The given function is f(x)=8x2-x3

Q: 2x at x =1 y = Зх-1

A: Find dydx as follows. y=2x23x-1dydx=22x3x-1-3x23x-12dydx=23x2-2x3x-12 Find dydx at x=1 as follows.…

Q: Find the slope of the tangent line to the curve y 5x at the point (-7, 245). A 70 25 -7 -70 E) 7

A: As we know that; The slope of the tangent line to the curve at a given point Px,y is equal to the…

Q: Find all points on the semicircle, y=sqrt 7-x^2, at which the slope of the tangent line is equal to…

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Q: ) Find an equation of the line tangent to the curve y = x²e²-3 at a = 3.

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Q: Find (and simplify) the equation of the tangent line to the graph of

A: Equation of Tangent line to curve y=3xx-1, at x=2

Q: Find the slope of the tangent line to the curve - 2x2 + 4ry – 3y - 63 at the point (3, 3).

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Q: At the given point, find the equation of the tangent line, as requested. y^4+x^3=y^2+11x, tangent…

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Q: Find the point of tangency and write the equation of the tangent line at this point. B

A: The tangent to a circle is defined as a straight line that touches the circle at a single point. The…

Q: Determine an equation of the line tangent to the graph o

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Q: Find an equation for the line that goes through the point (0,0) so that the tangent of the angle it…

A: Given, (x1,y1)= (0,0) tangent of the angle it makes with the x-axis=0

Q: What is the equation of the tangent line to the curve y=−5x^2+4x+7 at x=-1? Write the answer in…

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.