Determine where the function is concave upward and where it is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) g(x) . = -x + 4x + 1 concave upward DNE concave downward

Q: Find the distance between the two values of x at which the function is discontinuous. x²- 3x + 2 2.…

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Q: write the function in the form y = ƒ(u) andu = g(x). Then find dy>dx as a function of x.

A: the given function is: y=x28+x-1x4 we have to write the given function in the form y=f(u) and…

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

A: We first find f"(x) using the power rule

Q: x = t3 − 12t,    y = t2 − 2 find d2y dx2 and for which values of t is the curve concave…

A: We find dx/dt and dy/dt.

Q: Use your calculator to make the graph of f(x) = x³ - 5x. df (a) Is- positive or negative at x = 2?…

A: The given function is f(x)=x3-5x

Q: B-Test and proof the function So(x In x)? dx

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Q: write the function in the form y = ƒ(u) and u = g(x).Then find dy/dx as a function of x. y =…

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Q: Q5: Find for the following functions: dx (1) In(x - y) = xy + y³;

A: We have to find the dydx of the given function.

Q: If L(f(x) – 2g(x))dx = 12 and g(x) = x, find f(x)dx. Hint: draw a sketch of g(x)! %3D

A: We have ∫28(f(x)-2g(x))dx=12g(x)=xWe have to find∫28f(x) dx

Q: Hiw Find dy for the followng functions- 1-5x +X 2+x 3. y= lacsinfe}} %3D

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Q: Write the function in the form y = f(u) and u = g(x). Then find dy as a function of x. - 12x y = e

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Q: Q1 : for v = -3xy2 +x3, check the function for harmonic and then find f(z)

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

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Q: Find dy for the following functions. y=6x2

A: We have the given function as   y=6x2 We have to differentiate it

Q: Does the function I(x. y) is harmonic ? Q5) Evaluate: So So x+1) dzdydx

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Q: find the derivative:  c(x)=(x2)500x (the choices are in the image bellow)

A: This question is based on Chain rule differentiation. d/dx {f(x).g(x)} = g(x).d/dx{f(x)} +…

Q: P = 6x + sq. root of x where x is the number of magazines you sell in a month. If you are currently…

A: Given p(x)=6x+x  where x is the number of magazines you sell in a month.

Q: Find for the following function. dx2 y=e -6x2 %3D dx2

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Q: Plot the following functions over the interval 0<x<4 in the same a) x3 plot: b) e* c) ex2

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Q: The domain of the function f(x)= tanh( - 23) is (A, 264)

A: Given,          The domain of the function fx=tanh-1xk-23 is A,264.

Q: (x* + 2ху — 4y?)dx — (x? — 8ху — 4у?)dy %3D 0 -

A: Explanation of the answer is as follows

Q: of af For the function f(x.y)= 7x-9y- 3, find and dy

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Q: 2. (x? + 2ху — 4у?)dx — (x? — 8ху — 4у?)dy %3D0 -

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Q: Find for the given function. w= 10z2 e?

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Q: write the function in the form y = ƒ(u) and u = g(x).Then find dy/dx as a function of x. y = e-5x

A: Given function:

Q: For what value of x does the function g(x) =--x³ + 2x? strictly concave downward? А. x> 2 В. х>1 С.…

A: Use the property of strictly concave downward i.e.g"(x) &lt;0.

Q: Find dx for the functionf (x) = /cosh(x+ 8) T5. Select the correct answer. |

A: We will apply the power rule and the chain rule.…

Q: 4. Given a function, fix), such that f(x)dx = 10, calculate: a) - r(«)dx b) S rx - 2)dx d) Stsx) +…

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Q: write the function in the form y = ƒ(u) and u = g(x).Then find dy/dx as a function of x. y = e2x/3

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Q: write the function in the form y = ƒ(u) and u = g(x).Then find dy/dx as a function of x. y = e5-7x

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Q: Use the chain rule to find the derivative of f(æ) = 3e10a° + 9x° f' (æ) Add Work Check Answer

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Q: Determine whether the following statementsare true and give an explanation or counterexample.If in…

A: we know that for any given function ∫abfxdx=-∫bafxdx which means given statement is false

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

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Q: Q:A- Find for the following functions: - 1+x* 1- 1+secy

A: Given: xy21+secy=1+x4 For finding dydx, we simplify given expression then differentiate it

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

A:

Q: x+1 At what points is the function y = continuous? x2 - 6x + 5

A: To solve this problem we will use the concept of continuity of rational function.

Q: Write the function in the form y = f(u) and u = g(x). Then find as a function of x. dx y= e - 10x…

A: Given that:y=e-10xTo find dydx

Q: Let f(x) = x² – 4x – 5, x > 2. Find the value of df-1/dx at the point x = 0 = f(5).

A: (f-1(x))' = df-1dx = 1f'(f-1(x))

Q: - JH is a midsegment of AKLM. Find the value of x. x+7 H. J

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Q: Find a function F(x) for which F(0)=7 and df/dx= 9ex -2sinx+3x

A: GivendFdx=9ex-2sinx+3x

Q: mat ftoydk = hat f(x)dx: 1 Find the 2 a

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Q: Suppose y=f(x) is an even function. If , f(x) dx =7 and 25 So f(x) dx 25 16, find the value of S…

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Q: For the function y = x² + 2x, the value of dy when x=3 and dx=0.1 is (А) 0.15 B - 0.8 -0.15 D 0.8

A: The given function y=x2+2x  ;  x=3 and dx=0.1

Q: Let f(x) = 8x – 15x2 – 3, x2 1.5. Find the value of df -1 at the point x =1185= f(6). dx

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Q: (x) is an even function, and if f 6 f(x) dx = 15, find f³, f(x) dx.

A: Given query is to find the value of the Indicated integral.

Q: write the function in the form y = ƒ(u) and u = g(x).Then find dy/dx as a function of x. y = (4 -…

A: This function is the composition of two functions, namely Therefore,

Q: Q3: Find for the following functions: - dx csc-/3 5x

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Q: Determine the following a) f(r² -x=1)dx

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Q: Use the definition to find L{f(t)}

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Q: he surtace f(xy) A

A: A line lies on a plane if and only if every point on the line, lies on the plane and the normal to…

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.