f(x) = from x = 1 to x = 6 using 5 approximating rectangles and right endpoints. Estimate = (B) Repeat part (A) using left endpoints. Estimate =

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A:

Q: 2 * (1+x²)?" -00

A: Answer

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A:

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Q: Зх-1 5. y = 2х+5

A: We will find the derivative by using the delta function.Below find the solution with details…

Q: derivative of f(x)= 1/(x^2+5) is

A: Given,          fx=1x2+5

Q: 4. Find the slope of the tangent to the graph of f (x) = x³ + 3x² + x at its point of inflection.…

A: Slope of the tangent is obtained by dy/dx

Q: How is derivatives utilized in solving for the dimensions and total area of a box?

A: Here we to write how is derivatives utilized in solving for the dimensions and total area of a box.

Q: pret 30. f(x)= e2! dt 2-x

A: Given that: f(x)=∫2-xxexe2tdx

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A: Solution is given below:

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A: Consider the function  f(x) = 12x2− 9x + 15 point (−2, 81).

Q: What function should be used to minimize the distance between, y = 3x2, and the point (0, 2)?

A: y=3x2,  0, 2.

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A:

Q: Use the Second Derivative Test to find all relative extrema. h(t) = -x + 6x² - 4

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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 at point (-2,2) on the curve f(x) = 2 x2 + 3x using First…

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 5 - -2, and the line 4…

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A:

Q: (8 points) Find the slope of the line tangent to the graph of 1 f (x) = 2x* – 32x + 17x2 – 9x + 4 at…

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Q: F(x) = -7+ x2 INTERUAL-ピ-3 -2. AUERAGE RATE of

A: Given query is to find the rate of change for the given interval.

Q: Find derivative using quotient or product rule

A: Given function can be written as Now, we use quotient rule of differentiation to find derivative

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

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A:

Q: Find the slope of line drawn tangent to the function. f(x)=x2+7, at the point (-2,11) by using the…

A: Shape of tangent line to the curve is given by first derivative of curve at given periodDerivative…

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A:

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A: We have to find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis…

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A: The objective is to find the equation of tangent line.

Q: A piece of wire, 370 cm long, is to be bent into an isosceles triangle. What should the exact…

A: given: A piece of wire, 370 cm long, is bent into an isosceles triangle. we have to determine what…

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Q: Show that the rate of increase in the slope of the tangent at a point on the curve y = 2x3 is 12…

A: Consider the given curve: Here the objective is to show that the rate of increase in the slope of…

Q: Find derivative using product or quotient rule

A:

Q: Find an estimate for the positive root of x³-x²-x+1=0 using seven iterations of the Fixed-Point…

A: The following steps are used to find the numerical solution of the equation fx=0 by the fixed point…

Q: Find the slope and an equation of the tangent line to th 3 2 3. f(x) = + 8x + 8; (-1, 21 slope 11…

A: Recall: Point-slope intercept form :  y-y1 =m x-x1 where , 'm=dydx' is the slope and x1,y1 are given…

Q: Use the second derivative test to find all relative extrema  f(x)= x+4/x

A: The given function is as - f(x) = x+4xProcedure to find local extremas - 1. Find f'(x)2. Put f'(x) =…

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A:

Q: Apply the first derivative test to indentify all relative extrema. f(x) = ¹²-2x+1

A:

Q: f(x) = (6x – 7)(2x + 3) %3D

A: Given  f(x)=(6x-7)(2x+3)

Q: 5. Use the Second Derivative Test to find all local extrema of the function below. (3 points total)…

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A:

Q: Differentiate f(x)= (3x+2)^(arctan(x))

A: We can solve this problem using logarithmic derivative.

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Q: Approximate fls 3 + 2x* using Simpson's rule (n=6), then find the percentage of error after…

A: nhbgk

Q: fa) =x3-6x*+15x-2, Please find for the tangent line to f "x) (8,1)

A:

Q: Use the second derivative test to find the extreme values of the function f(z) = z-3z2-24z

A:

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.