Express the length I of a chord of a circle of radius 8 as a function of its distance x from the center of the circle.

Q: Estimate the slope of the tangent to the function… at the point of abscissa -3 and then determine…

A:

Q: The slope of the tangent line to the graph of the function y = 2/x – 6 at (36, 6) is 6 -0.50 0.17…

A:

Q: Find the equation of the tangent line to the function h(x) = xv4 + 2x at x = 6. %3D %3D

A: Differentiate the function with respect to x to find the slope of the tangent line.…

Q: By using differentiation, determine the width w that gives the maximum area A of the poster and show…

A: We have to find value of h & w for maximum Area.

Q: Find the slope of the tangent line to the graph of f(x) = x2 - x at (4, 12).

A:

Q: . Find the linear approximation of the function f(x) =  sqrt  (1-x) at a= 0 and use it to…

A: We find f(0) and f'(0) first  so the point is (0,f(0))=(0,1) and slope of the tangent= f'(0)=-1/2

Q: Find the equation of the tangent line to the graph of the function f (x) = (x² + 8) (x – 3) at the…

A: The gradient of the tangent at any particular point is given by :     f(x) = (x2 + 8) (x - 3)…

Q: find the slope of the tangent line to the graph of f at the given point f(x)=x^2-8x+2 at (2,-10)

A:

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 3x2 -4,…

A: The given function is fx=3x2-4 and the point is 3,23.

Q: . The domain of the tangent function is______

A: Domain is the input value for which given function is defined. We know that, tanθ=sinθcosθ Tangent…

Q: The domain of the tangent function is _____.

A: Domain of the function- If we have function f(x), then domain of the f(x) is set of the values of…

Q: Find the slope of the tangent line to the graph of the functiony=f(x)=−6.5x^2 at point x=7

A:

Q: Determine if the function f(x)=arctanx is convex downward or upward at the point x=1?

A:

Q: The slope of the tangent line to the graph of the function y = 9Va -2 at (4, 16) is -5.00 O -4.00 O…

A: Simply calculate the derivative of function at given point.

Q: The slope of the tangent line to the graph of the function (16, 24) is - O 1.25 O 0.88 O -2.00 | O…

A: Given function -  f(X) = y = 7√x -4

Q: Find all the values of x where the tangent line is horizontal. f(x) = 2x + 45x +324x +4

A:

Q: Find the slope of the tangent line that passes through point (1, 2) to the graph 8y³ + x²y O-2/97…

A:

Q: What is the length of the curve y = sqrt(4-x2) from x = -2 to x = 1?

A: y=4-x2 Differentiating with respect to x, we get dydx=124-x2·d4-x2dx   ∵dxdx=12x=124-x2·0-2x=-x4-x2

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 5 − x2 ,…

A: We find the derivative of f(x) using the power rule

Q: Find the tangent line of the function f(x) = - 4Vx at x = 4, and the point at which tangent %3D line…

A:

Q: Find an equation of the line tangent to thegraph of f(x) =3/x at (2,3/2)

A: Given: y=fx=3x, 2,32 for finding of equation of tangent at given point we need slopem of tangent at…

Q: Find the slope of the tangent line to the graph of the function at the given point.

A: f(x)=2x2-3⇒f'(x)=2·2x-0=4x

Q: The slope of the tangent line to the graph of the function y = 7Vx – 3 at (9, 18) is - O 3 - 2.00 O…

A: Simply take the derivative of the function at that point.

Q: the line tangent to f(x)=x' 3.

A: we have to find the equation of line tangent to  f(x)=x3-x2-5      , at the point (2,-1)

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 3x2 - 4,…

A:

Q: The slope of the tangent line to the graph of the function y = 9/x – 7 at (49, 56) is . O -1.14 O…

A: Given,  The function  y = 9x - 7   We have to find the slope of the tangent line at 49, 56.

Q: Find the tangent line to the graph of f(x)=(x+1)/(x-1) at the point (2,3)

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

Q: Find an equation for the line tangent to the graph of f at (3, 103), where f is given by f(x) = 5x³…

A: As we know that; The expression for the equation of the tangent line is: y-y0=mx-x0 Where m is the…

Q: ) Find the equation of the tangent f (x) = 4x - 8/x at a = 16. %3D %3D

A: Given: fx=4x-8x at x=16 For finding equation of tangent at x=16, we need to find y-coordinate for…

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 7x − 4x2…

A: Given, function

Q: Find the equation of the tangent line to f(x) = 8x² – 5x – 40 at (3,17). %3D

A: Solution of the problem as follows

Q: Find the slope of the tangent line to the graph of f(x) = x2 + x at (2, 6).

A: Given :fx = x2+x

Q: 5. State the domain and the range of the tangent function.

A: Consider the tangent function Give the domain and range.   Since tan x=sin xcos x therefore, tangent…

Q: Determine the points where the curve f(x) = 2x3 + 3x2 – 36x + 1 has a horizontal tangent. -

A:

Q: The slope of the tangent line to the graph of the function y = 7 x – 3 at (9, 18) is. O -2.67 O 1.17…

A: We know that dy/dx gives slope of tangent at any point.

Q: Find the slope of the tangent line to f(x) = √9x³ at the point x = 4.

A: We have to find the slope of the tangent line to f(x)=9x3 at the point x=4.

Q: Find a function that models the radius r of a circle in terms of its area A.

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Find the slope of the tangent line of f (x) = 2x² - 3x + 2 at x = 2 %3D

A:

Q: The ________ of a sine or cosine curve represents half the distance between the maximum and…

A:

Q: Find the tangent line to the equation: f(x) 3x2 + 2x-1, when x= 2 %3D

A: Using equation of tangent formula.

Q: Find an equation of the tangent line to the graph of the function (x)= Vx –7 at the point (23, 4).

A:

Q: Find the points on the graph of f(x)=48x−x3 where the tangent line is horizontal.

A: Given:f(x) = 48x – x3.Compute the derivative of the function f(x) as follows.

Q: The slope of the tangent line to the graph of the function y=7V=-3 at (9, 18) is O 1.83 O-2.67 O…

A:

Q: Determine the line tangent to f(x) = 2x2 + 3x + 1 at (-2, 3).

A: The tangent line to a curve at a given point is the line which intersects the curve at the point and…

Q: By total differentiation, determine or find the approx. change in the length of the hypotenuse of a…

A:

Q: Determine the equation of the tangent of the function, f(x) = 4−x / x+2 at x = 2.

A: According to question,Given function,fx = 4-xx+2

Q: The slope of the tangent line to the graph of the function y = 8vT- 4 at (16, 28) is O 1.00 O -2.25…

A:

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 2x2 − 3,…

A:

Q: The slope of the tangent line to the graph of the function y = 7VI - 3 at (9, 18) is O -2.00 O 1.83…

A: Solution

Q: Find the slope of the tangent line to the graph of the function at the given point. F(x) = 2x2 – 5,…

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.