H.W Is f (x) = x. |x| differentiable function? %3D

Q: Let I = f(x) dx, where fis the function whose graph is shown below. y f 2. 2.

A: Here is the solution of the given problem. Riemann Sum

Q: Find the absolute extrema of the function on the closed interval.

A: Differentiate the function h(t)=tt+3 by using the property…

Q: define y as a differentiable function of x,  find the value of dy / dx at the given point. (x3 - y4)…

A: Given : Define , y as a differentiable function of x . The equation is ( x3 - y4 )6 + ln ( x2 + y )…

Q: What is the range of the function y = cos™+(x +1)? 0(-2,0] o [0, r] T O (0, T)

A: The range of basic inverse cosine function is 0≤cos-1x≤π. The range of y=cos-1x+1 is also…

Q: c. f(1) d. Is f differentiable at x = 3?

A: Given The graph of function f as  To find: c. f1d. is f differentiable at x=3?

Q: The volume V of a right circular cylinder of height h and radius r is V = πr 2 h. If the height is…

A: Given: The volume of a right circular cylinder is, V=πr2h . Here, h is the height of the cylinder…

Q: The temperature of points on a plate x2 + xy + y? <1 is modeled by the function f(x, y) = 25(x² +…

A: Given: The temperature of point on a plate x2+xy+y2≤1 is model by the function is : f(x, y)=25 x2+y2…

Q: Refer to the following figure, which displays a right circular cone along with the formulas for the…

A:

Q: COS X continuous? 3x At what points is the function y=

A: The given function y=cos x3x

Q: a² + y? – a*y³ f(r, y) x² + y?

A:

Q: 9) Where is the function h(t) = (t + 5)"3 differentiable?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: A spherical balloon with radius r inches has volume V(r) =Tr'. Find a function that represents the…

A: First, we are given the formula for the volume of a sphere…

Q: Where is the function differentiable ? |x|=?|x+h|=? . x&lt;0

A: to find differentiability of function x

Q: The volume V of a right circular cone is V = (1/3)πr 2 h. If the height is twice the radius, express…

A: We have to express the volume V of a right circular cone as function of r if height is twice the…

Q: The volume of a right-circular cone of radius r and height h isV = π/3 r2h. Suppose that r = h = 12…

A: Consider the given: Volume,V=π3r2hr=h=12 cmDifferentiate w.r.t. "r",dV=π32rdrh    ⋯⋯11cm increase in…

Q: If y is a twice differentiable function and x cos y + y cos x = t, find y"(0).

A: solve by differentiate

Q: Suppose that the radius r and volume V = Tr³ of a sphere are differentiable functions of t. Write an…

A:

Q: Determine all points at which h(x) is differentiable. Justify your answer. 9 – x2

A:

Q: At which r-values is the following function g differentiable? Explain and compute, where necessary.…

A:

Q: AP to Suppose that the radius r and volume V = 4Tr³ of a sphere are differentiable functions of t.…

A:

Q: The volume V of a right circular cone is If the height is twice the radius, express the volume V as…

A: The height is twice the radius

Q: f'(rr), where f(t) = sint cost

A: Given function is ft=sint cost To find: f'π Solution: Product rule of differentiation is:…

Q: Find the critical local extreme points (if any) to the function -2x3 f(x, y) = + y? + 8x — 6у 3 Vour…

A: We will find out the required critical local extreme point.

Q: The volume V of a right circular cylinder of height h and radius r is V= π r 2h. If the height is…

A: Volume of a right circular cylinder = V = π r2 h where r is radius of cylinder  and h is height of…

Q: Evaluate dy and Ay for the function below at the indicated values. y= f(x)= 44 1-- x- 2, dx Ax = -…

A:

Q: The volume of a right circular cylinder with radius r and height h is V = πr2h. Is the volume an…

A: Given: Volume of a  right circular cylinder =  πr2h  To determine: Is the volume an increasing or…

Q: (a) Define what it means by for y = f(x). %3D

A: In this question we have to define the meaning of dydx for y=fx

Q: Find the absolute extrema in the interval [-PI ,PI] of y = 2cos x .

A: topic - extrema of the function

Q: Suppose that y is a differentiable function of the variable x. Find y' D↓x y of 5x³y-7xy² = 3 +7y

A: Given that:5x3y-7xy2=3+7yTo find Dxy or y'

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

A: Answer

Q: . What effect does a vertical stretch or compression have on the y values of a function? What effect…

A:

Q: Determine the values of x at which the function in Figure  is: (a) discontinuous and (b)…

A: To determine the values of x at which the function is  a) discontinuous. b) nondifferentiable.

Q: Sketch the graph of y = v4-x², - 2<x<2. a

A:

Q: The area of a disk as a function of radius is given by A = πr². How close must r be to 2.0 cm to…

A:

Q: The temperature of points on a plate x + xy+ y² < 1 is modeled by f(x, y) = 25(x² + y²). Find the…

A:

Q: It y is a twice differentiable function and xcosyt y cosx =C, find y"(0)

A:

Q: Find the critical points, points of inflection, concavity and the local and absolute extrema for the…

A:

Q: Consider the function f(x) such that (a) f(8) = 24 and (b) the tangent line at (x, f(x)) has slope…

A:

Q: Is y = |x| differentiable at x = 0? Justify your answer.

A: We are asked to check the differentiability y=|x|  at x=0

Q: Sx? -1, x <3 f(x) = Continuous at x-3 ? (2ax , x 23

A:

Q: Examine this figure showing the graph of y = f() y = f(x) (10, 4) Tangent line (4, 2) and estimate…

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Q: Q4:Find the relative extrema of f (x) I+3 I- 2

A:

Q: Find where f(x) is increasing, decreasing, and find local extrema.

A: Differentiate the function fx=x2x2+1 with respect to x, to find f'(x) an f''(x).…

Q: 3 In x x² x > 1 f(x) = 2 x² + 3 – 1, x <1

A:

Q: Q3) State the approximation for a differentiable function f(x): (a) V51 (b) V123 (c) (33)

A: (a) 51 Linear approximation is obtained as Lx=fa+f'ax-a Consider the function fa=a. On…

Q: Find the point on the curve f (x) = Vx that is closest to the point (2,0). Put your answer in the…

A: Use distance formula and differentiate and put zero

Q: Match the shaded region that would describe the domain of the function z = F(z, y).

A:

Q: Determine where the function is (a) increasing, (b) decreasing, and (c) where the relative extrema…

A: Given:- F(x) = 21/√x To find:-  (a) increasing (b) decreasing. (c) where the relative extrema occur.…

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.