For each of the following, find all values of z (if any) such that the tangent line Question 7 of the graph through (x, f(x)) has slope 5. For each of these values (if any), find the equation of the tangent line through (r, f (x)). a) f(e) =D알 - 3x2 + 14x+ 100 b) f(z) = ;r° 2 + 3x + 103 %3D 112

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A:

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A: Equation of a line having slope m pass through the point (x1,y1) is       (y - y1) = m (x -x1)

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A:

Q: (a) The curve with equation y 2   = x3 +3 x 2  is called theTschirnhausen cubic. Find an equation of…

A: We find dy/dx at x=1 and y=2  So the slope of the tangent = 9/4

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Q: 19. Which of the following illustrative equations will give a slope 10 of the tangent line to its…

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Q: 1 The slope of the tangent line to the graph of y = at a = 1, is 3e². %3D e (r + 2) Select one: a.…

A: Given curve: Now,

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A:

Q: 3. Write an equation for the tangent line to g(1) at I=2 if g(2) = 7 and g'(2) = –3. %3D

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Q: Find the equation of the tangent line at the given point on curve.

A: According to power rule of differentiation ,ddx(xn)=nxn-1 and and according to product rule of…

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Q: Find the equation of the tangent line to the graph of a+ y = 3 at the point (1,4). 1) y - 4 = 2(x -…

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Q: Find the coordinates of the points on the curve y= x' + 5x + 3 at which the tangent: makes an angle…

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Q: Find an equation of the tangent line at the given point. xy + x2y2 = 6, (2, 1)

A: We first find dy/dx at x=2, y=1

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Q: (1) Find the equation of the curve given the slope of its tangent line (mr) and the point P(a,b)…

A: Solution is below

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A: Derivative y with respect to x and then substitute the given point to find the slope.

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Q: The equation of this tangent line can be written in the form y = mæ + b where: m is: b is:

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Q: Find the equation of the tangent line to the curve (a lemniscate) 2(x + y°)´ = 25 (x² – y²) at the…

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Q: find an equation of the tangent line at the given point. xy + x2y2 = 6, (2, 1)

A: Our Aim is to find an equation of the tangent line of the given pointxy+x2y2=6 -(i) at…

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A: We have to find

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Q: 4) Find a formula for the line tangent to the curve at the point (4,4).

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Q: what is the equation of the tangent line to the graph of xsin(xy) = (√2)/2 at the point (1, pi/4)

A: iven:xsin(xy)=12

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Q: The slope of the tangent line to the curve C at the point (1, 2) is A) 4 B c) 2 D - 4 2.

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Q: find (a) the slopeof the curve at the given point P, and (b) an equation of the tangentline at P. y…

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Q: aph of given equation at (1,-1/2)

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A: The equation of the parabola is y=2x2+2x+7

Q: The slope of the tangent line to the graph of y = In(ry) at the point (e, 1) is .2 Select one: a.-e…

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Q: find (a) the slopeof the curve at the given point P, and (b) an equation of the tangentline at P. y…

A: Given: y=7-x Differentiate given equation with respect to x we get, dydx=-127-x Now at the point…

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Q: The slope of the tangent line at any point (x, y) on a curve is 2A If the point (9, 3) is on the…

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Q: The curve defined by the equation x^2+y^2=(2x^2+2y^2-x)^2 is called a cardioid. Find the equation of…

A: consider the given equation, x2+y2=2x2+2y2-x2 Use implicit differentiation method and differentiate…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.