• Find the domain and range of the following function · f(x) = |x| – 2 f(x) = [sgn(x – 1)] 1 • y= x2+2 · y = Vx? – 9

Q: Compare the values of delta y and dy for the function f(x)= x^3 - 3 at x=3and delta x= 0.2

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Q: The critical point of the function* f(x, y) = x² + 5y² + 2 cos x

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Q: 1) Find the value of C that make the function continuous at x-1? x 1 -

A: We have given piecewise function  Function is continuous at x=1 if  f1+=f1=f1- f(x) = C-x        if…

Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

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Q: Given the function h (x) = : x+1 Over what interval(s) is h (x) decreasing?

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Q: (a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

A: Consider the given piecewise function

Q: For which x value does f (x) = x - 3x2 + 1have a local maximum. CO C-1 C 1 C -2 C 2

A: Given: The function fx=x3-3x2+1, To find: point of Local maximum

Q: Find the Wronskian for the set of functions.{e3x, sin 2x}

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Q: 2. The difference between the greatest and least values of the function T T f(x) = sin 2x - x on - 2…

A: Greatest and lowest value may be differ from local maximum and local minimum in a closed interval.

Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

Q: If f(x) is an even, continuous function for which = 4 and dx = 4, then f (x) dx 3 2

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Q: Find the absolute maximum and absolute minimum of f(x) on the given interval f(2) = (-1,2) %3D x²…

A: 1) fx=x2x2+1, -1,2 Differentiate f(x) with respect to x…

Q: 4. Determine all possible functions f(x) that satisfy the given conditions. (a) f'(x) = V¤ – 3 x2…

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Q: 1) Find the absolute extremum values of f(x) = x² [1, 2]. – 2x + 12 over the interval

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Q: 7. For what value of the constants A and B is the function f continuous on (-0o, 0)E AV-x+6-1 for x…

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Q: 5. Consider the function h(x) whose derivative h' (x) = 3x2Vx3 + 8. (a) Find functions f and g such…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval: f(x)= square root…

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Q: Let f(x)=4+ln(x2+3)f(x)=4+ln(x2+3) be a function defined on the interval [0,∞)[0,∞). Find the…

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Q: 1 For a function f(x), we have f(x) = 1+ x? and f(0) = 0 prove that x +y f(x) +f(y) =f 1-xy

A: We will prove as following.

Q: Find f′(x) and f′(c). Function f(x) = x cos x Value of c = /4

A: The given function f(x) - f(x) = x cosxDifferentiation on both sides with respect to 'x' to get the…

Q: Find the absolute maximum and absolute minimum of f(x) on the given interval f(x) = 2x2 – 4.x +3,…

A: To find the absolute minimum and maximum of a continous function on the closed interval [ a, b ], we…

Q: 1. If F(x)= = ² e²² et² dt, find F(1) and F'(x). ez

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Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

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Q: Determine all critical points for the function. T(x) = x3 - 3x? + 8 O A. x= - 1 and x = 1 O B. x= 0…

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Q: 2. Consider the function f(x) = 1 – x², z ER. Draw the graph of f and calculate the equation of line…

A: solve the following

Q: Find the dérivative of the function: f(x)=In(e^x-13x)

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Q: 25. The function g(x) = [", |u| du is not differentiable at x = 0.

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Q: 1. Is a function f(x)=√x differentiable at a) X = 1 b) X = 0 c) X = -1

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 1. Where are the following functions continuous? x F(x) = ex + 4-x3 G(x) = 3x5 - 4x? H(x) = x-5x3…

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Q: Q3) If the function (2x + 1 +2 x > h) XSh f(x) having limit at x = h. Find the value of h. Q4) f(x,…

A: Our objective is to solve the above questions.

Q: If g(g(x)) is continous at 0, then g(x) is continous at 0.  True or False?

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Q: 1. The range of y=-e* +2 is (-0,1). 2. The function f(x)=sin x+cos x is an odd function. 3. lim

A: Topic:- function  Topic:- as per our guideline only first three subparts need to be answered.

Q: [ 2 sin(;) 15. Given that f(x) =- ki, is a continuous function at z = 0, the value of k is x = 0 B !…

A: A function f(x) is continuous at x=a, if right hand limit = left hand limit = function value at x=a…

Q: 2. Find the derivatives of the following functions. 4 a. f(x) = 3x³ x2 b. f(x) = (4 – x²)" C. f(x) =…

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Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: 3. Find constants A and B such that the function x2 f(x) = if x 2 is differentiable at x = 2.

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Q: 4. Find the local maximum and minimum values of f,using both the First and the Second Derivative…

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Q: Consider the following function: f(r) = 2r + 3z² – 12z Find the critical numbers of f. (x = ?)

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Q: Q2: Is the function f(x) = sin x -2x + x' odd or even Odd function C Even function C Not of all O

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Q: a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

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Q: Find the derivative of f (2) = xe 2 o f (2) = e * (e – 22) z- O f (x) = x°e-2# (;- 2) O (E) None of…

A: The product rule of differentiation states that d dxfg=fdgdx+gdfdx, where f,g are functions of x.…

Q: 7. Find all values of x on the graph of f(x)=(x-1)´(2x+1) at which the tangent line is horizontal.…

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Q: (1) Locate the absolute extrema of the function on the closed interval. (a) y=4 sin x, [0,2n] (b)…

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Q: 2. Find the principal part with respect to x for x 0 of the infinitesimal f(x) = = Vx + Vx. (That…

A: We have to use expansion of the function after some manipulations.

Q: Use differentials and the graph of f to approximate    (a) f (1.9) and (b) f (2.04).

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Q: If f is a quadratic function such that f(0) = 9 and f(x) x2(x + 1)3 dx is a ratianal.functian,,find…

A: This question is about finding f'(x)  at x=0  where f(x) is a rational function

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.