x2 Plot the function f(x) for -4

Q: Use the second derivative test to find all local extrema. f(x) = 2sinx + cos2x

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Q: Find the derivative f(x)= (sin h^-1

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Q: (a) Find the equation of the tangent line to the graph of the function f(x) = 3x² at the point (-2,…

A: (a)   Differentiate the function with respect to x is,   Substitute -2 for x in the above equation.

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. f(x) =…

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Q: 2. f(x) = sin(x) lim sin(x) - et x + 00

A: Calculate the limit and horizontal asymptote in the following way: (2).              f(x) = e-xsinx…

Q: 1. Using the First Derivative Test, explain why the function f(x) =-2x has no extrema on any open…

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Q: Find the equation of the tangent line to the function f(x) = 2* at x = 4. (Use symbolic notation and…

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Q: Determine the point(s) at which the graph of f(x) =  -4x/square root of 2x-1   has a horizontal…

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Q: Find the equation of the tangent line to the function f(x) = 6* at x = 2 %3| (Use symbolic notation…

A: Here we have to find the equation of the tangent line to the function f(x)=6x ...................…

Q: Use second derivative test, If f(x) = 4x +9 then f(x) has a local maximum at the point 3. I= 3 I =…

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Q: a+sinx If the function f(x) is continuous at x-0, then a = 2+2acosx x<0

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Q: x cosx-sinx lim x2sinx 1 1/3 3 -1/3 4 -7 2.

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Q: Using the criterion of the first and second derivatives, find the graph of the function b) F(x) =…

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Q: cos2x- sin2x cos2x F(x)+C: What is Fx)? For dr = - 3 cosx - sinx

A: A detailed solution is given below

Q: f(x)=x+sinx / x2+cosx f '(x)=?

A: Given function: Now,

Q: FINAL EXAM Page 2 of 28 Previous Next If f(x) = 4x² +8x + 5, find f' (x) using the limit definition…

A: We have to find derivative.

Q: 3x2 tan x If f(x) find sec x f'(x) = Find f'(3)=

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Q: sinx Q1//A- f(x) = cosx x < Required: lim f (x) 4

A: To check the limit of the function at pi/4 , we check it's left hand limit and right hand limit at…

Q: x 2 sinx Q1//A- f(x) = x <= COSX Required: lim f(x) 4

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Q: If f(x) = tanh-1 then f'(x) =

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Q: Use the second derivative test to find the values of x where f(x) has local maximum or local minimum…

A: Consider the given function f(x)=cos(3x), x∈[-π/6, π/6]

Q: Find the equation of the tangent line to the function f(x)=6^x at x=2 (Use symbolic notation and…

A: At x=2  y=62 =36 So the point is (2,36)

Q: Cos“ x Find f'(x) if f(x) eT + V3x

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Q: x2 Let g(x) : Use the Second Derivative Test to locate any local extrema of this function. 1 %3D

A: To find local maxima and minima of the function if exists using second derivative test.

Q: b) Find the inflection points. 4. For the given function find the local extrema using the Second…

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Q: f(x)=5 sinx-x-1, x = 1.8

A: Given,        f(x)=5sinx-x-1, x0=1.8

Q: Range of the function f(x) = 2 sin(1/x) is

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Q: 8. Sketch the graph with details of the function below by using the first and second derivative…

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Q: f(x+Ax)-f(x) Use the definition of the derivative f'(x) = lim Ax-0 to find the equation of the line…

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Q: 5-x * tan(x) If f (x ) = -sec(x) (a) f'(x) (b) f'(5)

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Q: Find the first derivative f' and the original function f. "(x) = x' – 8x + 6, f'(0) = 5, f(0) = 8…

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Q: Find the derivative of the function y = 9x³ tan¬' (4x). -1 (Use symbolic notation and fractions…

A: We can solve the problem by 'By Parts' Rule.

Q: Find the equation of the tangent line to the function f(x) = 4* at x = 2. (Use symbolic notation and…

A: Given the functionf(x)=4x      ...(1)

Q: 2x' Vx Use the power rule to find the derivative: 3 1 f (x) = 2Vx+ 2x

A: From power rule of derivative we know that if y(x)=xn then y'(x)=nxn-1 We use the power rule of…

Q: 7 Find the derivative of f(x) = 2 - %3D Type your answer without fractional or negative exponents.…

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Q: Cosx f(x) = function is odd or even

A: A function f(x) is said to be even if f(-x)=f(x) and a function f(x) is said to be odd function if…

Q: cos2x – sin2x cos2x For -dr =-F(x) +C. What is F(x)? dr%3D 3 cosx - sinx

A: We have to find F(x)

Q: 2 find range of function f(x)= |cosx|-1

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Q: Consider the function q(x) = x" – 3x10 + 2. Use the second derivative test to find the x-coordinates…

A: Given qx=x11-3x10+2

Q: tanx If f(x)= | V1+ x² - for all x€[0, 1/2], then f'(x) equals 1+ ex 0.

A: The differentiation of an integral can be obtained by using the second fundamental theorem of…

Q: 7. State the formal definition of the derivative of the function f(x). Use the definition to…

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Q: Using the definition of the derivative 1. find S'(2) if f(x)=x 2. find f" if 2x

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

Q: Togaritnmic difterenti ation f(X) = (4x3+1) (x? +5)3 to find derivative f'(x) = (20 Use %3D

A: f(x)=(4x3+1)(x2+5)3

Q: 5. Find the second derivative of f(x) = arctan(2x"). (You do not need to simplify your answer.)

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Q: cos2x - sin2x cos2x / cosx - sinx) dx=1/3 F(x) + C. What is F(x)

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Q: 3π f (x) = tan (x + with h 3 at x = || - 4 180

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Q: sinx Q1//A- f(x) = COSX Required: lim f(x)

A: Given function is piecewise function so we have to evaluate the left hand limit and writer limited…

Q: Calculate the derivative for f(x) = (x+5)(x-1)(x-8). (Use symbolic notaion and fractions where…

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Q: 5. f(x) = / tan¯ (3x’)

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Q: For the function f(x) = xe-2x give intervals of increase/decrease and intervals of concavity.…

A: Let's find.

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.