How many lines are tangent to both of the circles  x2 + y2 = 4  and  x2 + (y − 3)2 = 1?   At what points do these tangent lines touch the circles? (Enter your answers from smallest to largest x-value.)

Q: For what values of x is the tangent line of the graph of parallel to the line y = 0.7? (If there are…

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Q: (a) Find all the points on the graph of (x² + y? + y)2 x² + y? that have horizontal tangent line.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

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Q: For what value of x does the tangent line to the curve y=7+3e^x−6x  is parallel to the line 8x−8y=9?

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Q: 4 Find all the points on the curve x2 + xy + y? = 3 where the tangent to the curve is a vertical…

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Q: FIND THE LENGTH OF THE CURVE y = In sec X from X = 0 to X = - 4

A: Given curve is y= lnsecx .  We have to find the length of the curve from x=0 to x=π4. Length formula…

Q: 4. At what point on the graph of y =x2 is the tangent line parallel to the line 2x – 4y = 3?

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Q: Find the lengths of the curves in y = tan x, -7/3 < x < 0

A: In this question, the concept of integration is applied. Length of curve The length of the curve…

Q: Find equations for the tangent lines to the graph at the given points. 7ху + x %3D 8, (1, 1) and (8,…

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Q: 1- Find the equation of the tangent to the 2(x + y?)? = 25(x² - y?) at (3,1)

A: As per Bartleby's expert answering policy, we can answer only one question, so kindly post the…

Q: Does the graph of Sx²sin (1/x), x ± 0 f(x) = lo, x = 0 have a tangent line at the origin? Give…

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Q: 2. For what values of the numbers a and b is the curve f(x) = eaz²+bx tangent to the line y = e at…

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Q: At how many different values of x does the curve y = x +2x have a tangent line parallel to the line…

A: Given equation of curve is Differentiating with respect to x, we get

Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4)

A: Equation of the tangent line

Q: At how many different values of x does the curve y =x+ 2x have a tangent line parallel to the line…

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Q: 4. At what point on the graph of y = ÷x² is the tangent line parallel to the line 2x – 4y = 3? A.…

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Q: The curve y = a x 2 + b x + c passes through the point ( 1 , 2 ) . The line y = 2 x + 1 is tangent…

A: Given that the curve passes through a point.

Q: At what point is the tangent line to the curve y3=2x2 perpendicular to the line x+2y-2=0? P= (?,?)

A: We have to find the point

Q: Find the points on the graph of x^2+2x+4y^2=4+y where the tangent line is horizontal

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Q: a point on the cor ve y=x² - 2x -3 at which is parallel to Find the tangent line the X-axis

A: Given query is to find the the point where tangent line paray to x axis.

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: Find the points where the line y=−3xy=-3x intersects a circle of radius 2 centered at the origin.…

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Q: The slope of the tangent line to the curve + 2y? = 2x² + y at the point (1, 1) is Select one: 3. O 2…

A: Explanation of the answer is as follows

Q: 6. Find the length of the curve y =-+ from x =1 to x=2. 9. 28x

A: The curve is given by the equation, y=x99+128x7  and the point is given from x=1 to x=2. To find :…

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: For what values of x is the tangent line of the graph of f(x) = 6x + 18x² - 143x+ 18 rallel to the…

A: Explanation and solutions is given below....

Q: Find the exact length of the curve. 1 y = 1 + cosh(8x), 0 ≤ x ≤ 1 8

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Q: Find the lengths of the curves y = sin -1x - √(1 - x2), 0≤ x ≤ 3/4

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Q: (2) At what point(s) will the tangent line to y = x? - 4x +3 be horizontal

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Q: What is the slope of the tangent line to cos(æ – y) = xe" at the point (0, ). O 1 -2 O None of these…

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Q: Find the length of the curve (Sketch and Solve) One branched of the curve 9y2=4x3 from x = 0 to…

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Q: At what point is the tangent line to the curve y = 2x perpendicular to the line x – - 2y – 8 = 0? -…

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Q: 7. Find the length of the curve y= x'+ I from x = 1 to x . 12x Give your answer as a simplified…

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Q: A curve like Y = is called a serpentine. 1+2x2 3 n equation of the tangent line to this curve at the…

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Q: 8 17

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Q: Find an equation of the tangent plane to the graph y = x² + 2xz at (1,3, 1). (Possible Answer: 4r –…

A: We have to find an equation of the tangent plane to the graph y=x2+2xz at 1,3,1.

Q: At what values of x on the curve y= 2x³+13x²+5x+9 does its tangent lines pass through the origin? In…

A: Given equation of curve: y=2x3+13x2+5x+9……1

Q: 9. At what point(s) on the circle x 2 + y? = 13 is its tangent line parallel to the line 3x – 2y = 6

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Q: At what point is the tangent line to the curve y = 6x² perpendicular to the line x + 2y – 8 = 0?…

A: Follow next step

Q: If the length of the curve y = 4 x7 from the point (0, 0) to the point (Xo, f(xo)) is L= 1 (145)*…

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Q: 5. Find the slope of the tangent line to the graph of r = 2-2cos e when 0 = に一2

A: We have given equation of graph r=2-2cosθ  We have to find slope of the tangent line to the graph…

Q: Find the slope of the line tangent to y = 3x(cos x) at (7/2, 7/2). A) -3/2 B) 3x/2 C) /2 D) -x/2

A: Consider the function  y=3x(cosx) Point : π2,π2

Q: 1- Find the equation of the tangent to the 2(x2 + y²)2 = 25(x² - y?) at (3,1) %3D

A: According to guidelines we should have been able to do only one question at a time #1

Q: Find all points (x, y) on the graph of y with tangent lines perpendicular to the line y = 4x - 5. (x…

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Q: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.

Q: 4) Find the equation of tangent I point line to the circle below at point (1,-3). * x² + y² – 2x –…

A: Consider the given equation of the circle, x2+y2-2x-4y-20=0 The equation of the tangent line passing…

Q: 1 Find the length of the curve ソ= 9 from x =1 to x=2. 28x7,

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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.