The point P(16,8) lies on the curve y=√(x)+4 Let Q be the point (x,√x+4).A.) Find the slope of the secant line PQ for the following values of x. (Answers should be correct to at least 6 decimal places.)If x=16.1, the slope of PQ is: and if x=16.01, the slope of PQ is: and if x=15.9, the slope of PQ is: and if x=15.99, the slope of PQ is: B.) Based on the above results, guess the slope of the tangent line to the curve at P(16,8).

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Q: Determine equations of all lines tangent to the graph of f(t) = t° /3+2t² +4t that have slopes of 1.

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Q: (a) If Q is the point (x, sin 16)), find the slope of the secant line PQ (correct to four decimal…

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Q: For what values of z does the graph of f(z) = 21 – 9z² – 60z – 1 have a horizontal tangent line?…

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Q: (3) Find the equation of the line tangent to f(x) = 2x³ - 2x2 +1 at x = 1. [Hint: f'(a) is the slope…

A: We find the slope of f(x) at x=1 by finding f'(1)

Q: 2. Let f(æ) = 2e* – 3x² /a, whose graph is given to the right. Sketch in the tangent lines to f(x)…

A: Graphed the tangents using a graphing calculator.

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A: Given curve: Now,

Q: The point P 4 20 lies on the curve y = - If Q is the point ,- find the slope of the secant line PQ…

A: NOTE: Refresh your page if you can't see any equations. . given points are

Q: The point P(4, 1) lies on the curve y = Vx - 3. (a) If Q is the point (x, Vx - 3), use your…

A: Given Point P =4,1 which lies on the curve y=x-3

Q: Let  f(x)=1/2x^2-1.  Find the slope  of the secant line that contains points P=(2,f(2)) and…

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Q: 1. The ellepse ax? + 3y2 =4 is drawn below. %3D い等)。 Find the slope of he temg ent at

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 2 Find the distance from the point B = [0 5 0 to the line 1 +t| 0 -3

A: Here we will find the distance between the given point and line,

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

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Q: The point P(7, -4) lies on the curve y = 6- (a) If Q is the point find the slope of the secant line…

A: (a) The point P(7,-4) lies on the curve y = 46-xNow we know that slope of the Sacnt line be m =…

Q: w = (2x – 7)(x +5)/ Establezca dw dw dx 2.

A:

Q: Find the coordinates of the point on the graph of y = x^2− x + 3 at which the tangent is parallel to…

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Q: 1. Suppose that the point A(4, 2) lies on the curve g(x)=√x and that B is another point on that…

A: We will use given function to find all values . Note : Maximum 3 subpart are allowed to be solved at…

Q: Q1. Find the length of the of the curve y -x2 X2 from x = 0 to x = 3.

A: Given curve is, y=13x32-x12 To find the length of the curve from x = 0 to x = 3

Q: 21. NP and PQ are tangent to circle M. NP = 2x-2x and PQ = x -2x + 16. Find the length of NP.…

A: Length of NP problem.....

Q: 1. In the open interval (0, T/2) , find the point where the slope of the curve is 4? y = tan x

A: Given function , y= tan x, we have to find at what point, slope of the the given graph is 4.…

Q: T Find the tangeut line to the curve 1 2rg+ 12 at the point (2. 1).

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Q: 8. The line y = -4x + b is tangent to the curve f(x) = 2x² – 8x + 12. Determine the value of b. %3D

A: The equation of the tangent at a point h,k on a curve y=f(x) is given by, y-k=f'(h) (x-h)

Q: The point P(8, −3) lies on the curve y = 3/(7 − x). (a) If Q is the point (x, 3/(7 − x)), use your…

A: a) The slope between (8,-3) and  (x, 3/(7 − x)) is  Using this we make the table  x slope 7.9…

Q: Consider the following. a) Verify that the given point (7,7) lies on the curve. x3 + y3 = 14xy b)…

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Q: After Identifying and sketching the curve for x2+25y2-4x+100y + 4 = 0, partimize the curve

A: Given: x2+25y2-4x+100y+4=0 To Find: i. Identify and sketch the curve.ii. Parametrize the curve.

Q: 5. Find the slope for f(x, y) = xey at P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: To find the slope for function f at point P in the direction of the line from M to N.

Q: Given that f(2) = -5 and f'(2) = 3, find an equation for the tangent line to the graph of y = f(x)…

A: we have to find equation of tangent line

Q: Find the length of one branch of the curve ay? = x3 from x = 0 and x = 5a. 4.

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Q: Given the function f 1x2 = 1 - cos x and the points A1p>2, f 1p>222, B1p>2 + 0.05, f…

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Q: 5. Find the slope for f(x,y) = xey at P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: 2 For the graph of f(x) = ax + bx +4, the slope of the tangent at the point (3, 1) is 5. Determine…

A: Given that        f(x) = ax2+bx+4

Q: 9. Find the points on the graph y = х-2 7x - where the slope of the tangent line is parallel to 28х…

A: Given-  Consider the graph y=7xx-2. To Find- The points on the above graph , where the slope of the…

Q: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

A: Solution:- The given curve is  x+xy=6  ......(1) and point (4,1) we have to find equation of the…

Q: 11. Find all points (c, f(c)) 9. on the graph of f(z)= x³ – 3x² where the tangent line has slope

A: Given,       f(x) = x3 - 3x2       slope = 9

Q: The point P(9, -3) lies on the curve y 3/(8 x) (a) If Q is the point (x, 3/(8 - x)), use your…

A: To estimate the slope of the tangent and write down its equation

Q: The point P(9, -2) lies on the curve y = 8 - x (a) If Q is the point x, find the slope of the secant…

A: Given :- The point(9,-2) lies on the curve y=2/(8-x)  To find:- a if Q is tha point (x, 2/(8-x)),…

Q: Find the values of a and b for the curve x2 y + ay2= b if the point (1,1) is on its graph and the…

A: Find the slope of tangent line

Q: 20. Find the equation of the curve for which y" = x, and which through the point (1, 2) and the…

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Q: Find the slope of the curve at the given point.   9y^9+4x^7=7y+6x at ​ (1,1)

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Q: The point P(4, -2) lies on the curve y = 2/(3 – x). (a) If Q is the point (x, 2/(3 – x)), use your…

A: the slope of the line is given by

Q: At what point (s) is the tangent line to the curve y²=2x³ perpendicular to the line 4x-3y+1=0

A: Given y2=2x3⇒ y=2x3

Q: Find y' and the slope of the tangent line to the graph of (3x - 4y)7 = 2y2-7 at the point (3,2).…

A: The slope of equation is defined in terms of m=dy/dx

Q: The point P(S, -2) lies on the curve y = 2/(4 - x). (a) If Q is the point (x, 2/(4 - x)), use your…

A: Given P(5,-2) lies in the curve y=24-x

Q: A curve on the ry-plane passes through the point (0, a) for some number a, and has the property that…

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Q: 2. Consider the function y(x) = 5x² over the interval [0, 10]. (a) If the points A(0, y(0)), B(5,…

A: As per guidelines, we will solve first three subparts; Given function is yx=5x2  over the interval…

Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y

A: Given problem is : Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn…

Q: The point P(4, -2) lies on the curve y = 2/(3- x). (a) If Q is the point (x, 2/(3- x)), use your…

A: Here is the solution of the given problem one by one.

Q: Find the value of 'a' for which the tangent to the curve ƒ(x) = (a + 2) x³ − 3ax² + 9ax − 1 never…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.