2. Use the following graphs to insert < or > between the quantities in the boxes to form true statements. a. b. (8,5) (3,2) f(8)-f(3) f'(8) Using the right endpoints of the rectangles: 8-3 f(8)-f(3) f'(3) So f(x)dx 8-3 Using the left endpoints of the rectangles: f"(x) 0. S f(x)dx

Q: Find the equation of the tangent line of y = 6e* at xo = 0. (Use symbolic notation and fractions…

A: The given function is y=6ex, to find the equation of tangent at the point x0=0

Q: Find the equation of the line tangent to the graph of f(x) = -3 cos (x) at x 2

A:

Q: Suppose that f(x) is differentiable for x > 0, y = 2x + 1 is the tangent line to the graph of f at x…

A:

Q: Find the equation of the line tangent to the graph of f(x) = – = -3 cos (x) at x = 3 m(x – xo). You…

A: given: the function f(x)=-3cos(x) the point is x=-π3

Q: 4. Write an equation of the tangent line to the graph of f (x)=3x+8x at the point where x= 9.

A: Given query is to find equation of tangent to the f(x).

Q: Make a table using multiples of p/2 for x between 0 and 4p to help sketch the graphof y = x sin x.

A: given: y=xsinx use the fact that  sinπ-θ=sinθsinπ+θ=-sinθsin2π-θ=-sinθ

Q: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

A:

Q: Find the equation of the tangent line to y = 7et at x = 3. (Use symbolic notation and fractions…

A:

Q: The equation of the tangent line to the graph of f(x) = Vx+1 At the indicated point (3,2) is:…

A: By using the derivative and slope intercept form required tangent equation is :

Q: Find an equation of the tangent line to the graph at the given point .

A: Given: fx=4xx2+6 We need to find the equation of the tangent line to the graph f(x) at 2,45

Q: 9. What is the equation of the line tangent to the graph of the function f at the point (1,1)? f (x)…

A:

Q: 4. A. Use the tangent line to find a linear approximation to the function f (x) = Vx near x = 64.…

A:

Q: Find the equation of the tangent line to the graph of y = f(x) at r = 3. %3D f(x) = In(x – 6|) y =

A:

Q: 34. Find an equation of the line tangent to the graph of f(x) = (2x – 1)(x + 4) at (1, 5).

A: The objective of the question is find the equation of tangent at the point (1,5).

Q: 14. Find the equation of the line tangent to the graph of f(x) = 2x3-x + 1 at x = -1. %3D

A:

Q: If tanh x = 12/13  find the values of the other hyperbolic functions at x

A:

Q: he line tangent to the graph of y=In(3x)+ 2x e at x =1 6

A: Equation of line is given as   y-y0 = dydxat x=1*(x-x0) Given,x0 = 1y = ln(3x) + e2x6y0 = ln(3x0)…

Q: Find the equation of the line tangent to the graph of y = 3x cos x at the point (π, −3π).

A: Given Data: Equation: y=3xcosx Point: (x1, y1)=(π, −3π) The derivative of the given equation of…

Q: For what values of x in [0,2pi] does the graph of f(x)= x + 2sin(x) have a horizontal tangent?

A: Horizontal tangent:The slope of a tangent of the graph of a function f (x) is df (x) ∕dx. For a…

Q: 2. Find the points on the graph of f(x) =- where the tangent line is horizontal. x2+2

A: Given f(x)=xx2+2we want to find the point on curve where tangent is horizontal

Q: -2, find an If g(x) = xf(x), where f(3) = 4 and f'(3) equation of the tangent line to the graph of g…

A: Consider the given function gx=xfx

Q: The slope of the tangent line to the graph of the function y = 8VI - 4 at (16, 28) is O 1.50 O -1.75…

A: Given function is, y=8x-4

Q: 5) Find an equation to the line tangent to y = (x +3)³ at x = -3.

A: as per bartleby guidelines  i can do only first question. please ask other question seperately.

Q: Find the slope of the line tangent to the curve at the given point. y = 3 cos x; x = 3 3/2 2

A: 1) Find the first derivative of f(x) 2) Plug x value of the indicated point into f'(x) to find the…

Q: Find the slope of the tangent line to the curve y = 3'¬^ at the point where X = 0. 2 In 3 00 O None…

A:

Q: Find the equation of the tangent line of y = 4e* at xo = 0. (Use symbolic notation and fractions…

A: y=4exSubstitute x=0y=4e0=4The point is (0,4)

Q: Does the graph of the function y = 6x + 3 sin x have any horizontal tangents in the intervalocce O…

A:

Q: (4) Find the equation of the line tangent to f(x) = 12√ - 2² at the point (4,8).

A:

Q: 15 Find the equation of the tangent line to the graph of f(x) at the point where x = 2 Vx3 – x + 3

A:

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…

A:

Q: Find the equation of the tangent line to the function f(x) = –3x² form y - 2x at the point where x…

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 equation of both the tangent lines to the elipse x^2+4y^2=36 that pass through the point(12,3)

A:

Q: Find an equation for the line tangent to the graph of f at (1, 14), where f is given by f(x) = 30 -…

A: Please refer the attached image for complete solution.

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

A: Equation of line with slope m and passes through point (xo , yo) is (y-yo) = m(x-xo)

Q: Find an equation for the line tangent to the graph of f at (2, 28), where f is given by f(x) = 5x³ –…

A: Given function is fx=5x3-5x2+8. To find an equation of tangent line to the graph at point 2,28.…

Q: Find the equation of the tangent line of y = 9e* at xo = 0. (Use symbolic notation and fractions…

A: The given function is:y=9exThe point is x0=0

Q: Find the equation tangent line at a=2 for f(x)=2x²-3x+1 O y=15x-7 O None of these O y=5x+7 O y=5x-7

A:

Q: What is the equation of the tangent line at 3x+1 0₁ = 1² of f(x) = ² 0, 2 X-2

A: The equation of tangent is :

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: For what values of x does the graph of f(x) = 3e*cosx have a horizontal tangent line? 4.

A: Explanation of the answer is as follows

Q: Find the slope of tangent to the curve y=sin 4x +3x at (5, 35). None O 7 O 3

A: Note :- Steps to find slope :- 1) Find the first derivative of f(x). 2) Plug x value of the…

Q: Compute f '(x) and find an equation of the tangent line to the graph at x = a.

A:

Q: Find a limit equal to (x2 – 8)dx. 3

A: The integral of some functions are given below. 1)∫x2dx=x33+c2)∫8dx=8x+c Use the above and find the…

Q: 5) Find an equation to the line tangent to y= (x + 3)³ at x =-3.

A:

Q: 7) Find the equation of the tangent line to the graph of f(x) = –sin(x) +3 at x = 4

A:

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: If the line tangent to y = f (xht (3, 7) passes through the point (1, -3), find ƒ ' (3) O f' (3) = 5…

A: As the tangent line is passing through points (3,7) and (1,-3), we get the slope of the line as…

Q: 5 7. Find the slope of the tangent line to the graph of y = x² at the point where x = –

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

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.