Q- Find Domain and Range of the function 1) y=v2- Vx 2) y = 2e-* – 3

Q: What is the equation of the curve that passes through the point (1, 3) and has a slope of 2 x+3 O 9…

A: Here we have to write the equation of the curve that passes through the point (1,3) and has a slope…

Q: What are the coordinates of the points in the graph of y² –x²+ 6x – 13=0 in which the tangent line…

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Q: what is the equation of the tangent line to xy-3y^2=1 at the point (4,1) Express numbers in eaxact…

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Q: What are the equation of line passing through (-1,3) that is tangent to the curve x^2 + 4y^2 – 4x –…

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Q: 6. Parallel to the line Y = = -}(x – 100) – 99, 3 4 passing through (1, 3)

A: Given query is to find the equation of the line passing through (1,3) and parallel to the line…

Q: Suppose that | f(z)dz = 2, | f(z)dz = 1, %3D [ 9(2)dz = - 5, | 9(2)dz - 2. Then, | (=) – g(2))dz =

A: Given: ∫25fxdx =2, ∫23fxdx =1, ∫25gxdx =-5, ∫23gxdx =-2 To evaluate:∫35fx-gxdx We know that…

Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: Find the image of the line x = 1 under (a) flz) = z²

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Q: Suppose that y is a function of x. Find if 2x°y 3 2y + 5. - -

A: We will find out the required value.

Q: 5 Find the equations to both lines through the point (2,-2) that are tangent to the parabola y = x²…

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Q: Find the area of a triangle bounded by the yy axis, the line f(x)=4−67xf(x)=4-67x, and the line…

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Q: Find the length of the curve defined by 2? = 2y3 from x = 0 to x = 4:|| %3|

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Q: Parallel to x + 2y = 0; (1, 2) on line

A: To find the equation of line paralley to x+2y=0 and (1,2) is on the required line.

Q: What is the equation of the line normal to f(x) = 5x5 – 2x at x = -1 %3D

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Q: Find equations of the two tangent lines to the graph of f(x) = x2 that pass through the point (-1,…

A: Topic - tangent lines to curve passing through Given point outside curve

Q: the tangent line to the graph (x^2 + 4)y = 8 at the point (2, 1).

A: Use formula of  equation of tangent  line

Q: 2) Find FCO), if it exits Punctien f(z) - 2 if x raticnal if x irraticnal

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Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=3−16xf(x)=3-16x, and the line…

A: GIVEN DATA: Triangle is bounded by the equation of line fx=3-16x                         line…

Q: Point X is equidistant from F and T. Furthermore, point Y is equidistantfrom F and T. Does that mean…

A: To check: Whether the point X and Y are equally distance from F. Given: The point X is equidistance…

Q: Find the point (s) on x = 3 - y2 that are closest to point A = (1,0).

A: Given: x = 3 - y2 and point A = (1, 0)

Q: 17. Passes through the point (2, 1) and is perpendicular to y = -x+ 3.

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Q: What is the length of the curve y3/2+4 from the point (1,5) to (4,12)?

A: To find: The length of the curve y3/2+4 from the point (1,5) to (4,12).

Q: The shortest distance from the point (5, 10) to the curve x2 = 12y is: 5.127 6.445 4.331 3.474

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Q: Compute the slope of the secant line containing the points (1, f (1)) and D) on the graph of f (x) =…

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Q: Find equations of the two tangent lines to the graph of f(x) = x- that pass through the point (-1,…

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Q: 1 If f(x, у, 2)- ôf then х— у—3z ду а. 1 (х- у-3-)2 b. -1 (х-у-3-)* С. 1 (х-у-3-)° d. 2 (х - у-3-)?

A: In Partial differentiation w.r.t y we treat x,z as constants.

Q: 7. Find the slope of the line tangent to the curve at the point (2,1). x²y + xy² = 3x %3D

A: 7. The equation is given by x2y+xy2 = 3x                                                ......(1)…

Q: What is the equation of the line tangent to the curvev= x² – 1 at the point -2,3) y = x+ O y=-4x +…

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Q: Find the slope of the curve y = 2x2-3x at point (1,3) O 2 O 3 O -2 0 1

A: We   have to find slope

Q: (1, if x 2

A: Using the given piece wise function, we can plot it in given intervals.

Q: Let (21, Y1) = (7,9), m = 3. Then the equation of the tangent line is O y = 3x- 20 O y = 3r - 16 O y…

A: Equation of the tangent line = ?

Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13= 0 in which the tangent…

A:

Q: Find the points on the curve y = 2x3 - 3x2 - 12x + 20 where the tangent line is a. perpendicular to…

A: Find the slope of the line y= 1- (x/24)

Q: What is the equation of the line tangent to the function y = 2³+7x² + 5x - 2 at x = 0? There can be…

A: Application of differentiation

Q: Find the slope of the curve at the point (2,3) * x³ 2x + 1 3/2 1 O 1/2 O 1/4

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Q: Evaluate S(z² + 3z)dz along the straight line from (2,0) to (2, 2) and then from (2, 2) to (0, 2).

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Q: If f(2) = 3 andf'(2)=-1, find the equation of the tangent line when x = 2 %3D %3D %3D

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Q: Determine the equation of the line passing through the point (3,22) which minimizes the area of the…

A: This question is based on application of Derivative. The two-point form of a line passing through…

Q: 1. Can Rolle's Theorem be applied to y = (x – 2)5 on the interval [0, 4]? Justify.

A: we will see how to proceed

Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

A:

Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

A: As we know that; The slope of the horizontal tangent line is zero or m=dydxPx0,y0=0 Given;…

Q: 4- х, хS0 10) Determine if the function y(x) =- 3x, is differentiable at x = 0. X>0

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Q: 1. Can Rolle's Theorem be applied to y = (x – 2)3 on the interval [0, 4]? Justify.

A: Check differentiability at x=2

Q: The line whose slope is 3 is tangent to the curve y=x² + 3x + 2 at the point, O (3,-2) O (-3,2) O…

A: The line whose slope is -3 is tangent to the curve y=x2 +3x+2 at the point. Here slope and line…

Q: What is the equation of the curve that passes through the point (0, 3) and has a slope at any point…

A: We have to find

Q: Encounter the critical points of f(x, y) = 16x3 - 9y2 - 36x2 - 12y + 6x - 27 and then denote each…

A: To find out the critical points and denote it's nature.

Q: Show that the line y = -10x + 20 is tangent to the curve y = x4 – 4x^3 – 5x^2 + 26x – 16.

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Q: Find equations of the two tangent lines to the graph of f(x): x2 that pass through the point (-1,…

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Q: Give exomple of o line ar equation s unknown

A: First we see the defination of linear equation then give the answer.