Let f(x) =/x +1,then f•f=

Q: Find f-1 if f (z) = iz + 1.

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Q: Find the first and second derivatives of the function. f(x) = In(x + 4) f'(x) = f"(x) I3D

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Q: find all critical points of the function f (x) = sin^−1 x − 2x

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Q: Compute the derivative of f (x) = x 3/2 using the limit definition.

A: fx=x32

Q: use the second derivative test to find the local exterma of the function  f(x) =x3-9x2-48x+72 on R

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Q: Use the second order derivative test to find local exterma of the function  f(x) =x3-9x2-48x+72 on…

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Q: Consider the function f(x) whose second derivative is f”(x)=5x+2sin(x). If f(0)=4 and f’(0)=4, what…

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Q: Find the derivative of f(x) = In(x² + 1) %3D

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Q: Use the first derivatives test to find local exterma of f( x) =x3 -12x on R

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Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

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Q: 7) f(x) = 3e In x %3D

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Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

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Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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Q: Find the global maximum and minimum of the function on the given…

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Q: Compute the derivative of f (x) = x 1/3 using the limit definition.                            (x +…

A: Given: fx=x13 To Find: The derivative of the given function using limit definition

Q: Determine the derivative of f(x) = ( In x )6 with respect to x. f'(x) =

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Q: 2. If function f(x) = 3²-12 is continuous at x=2, find f(x). x-2

A: We need to find f(x).

Q: The function f(x)=(2-x)/(3) is continuous at

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Q: 2) Let f(x) = x' +x² – 5x – 5. Use the second derivative test to classify the critical points.

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Q: Find the derivative by the limit process. f(x) = 14-x²

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Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

A: q- differentiate the function fx=logax from the first principle it is known that, according to first…

Q: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

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Q: Consider the function f(x) whose second derivative is f''(x)=4x+3sin(x)   If f(0)=3  and f'(0)=2…

A: detailed solution with explanation is given below

Q: Find the derivative by the limit process. f(x) = 10 – x2 %3D

A: We know that the derivative of a function fx is given by:f'x=limh→0fx+h-fxh

Q: Find the relative extrema of the function f(x)= x2+3x+4 using first derivative test.

A: fx=x2+3x+4 To find extrema of function.

Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

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Q: Consider the function f(x)f(x) whose second derivative is f''(x)=4x+3sin(x)f′′(x)=4x+3sin(x). If…

A: Consider the function f(x) It's second derivative is f''(x)=4x+3sin(x)If f(0)=3 and f'(0)=4   We…

Q: Find the global maximum and global minimum of the function f(x)=sinx−x in the interval [−π,π].

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Q: Suppose you are working with a function f[x, y] and you find that f(¹,0) [x, y] ƒ[1, 0]? Why or why…

A: Given: A function fx,y such that f1,0x,y&lt;0 for all points x,y.   To determine: Whether…

Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?

A: Suppose   are continuous function at then rational function is continuous at   if .

Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: Let f'(x) = 100x(2x+3)(x-5), use the first derivative test to determine the location of the local…

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Q: Find the derivative by the limit process. f(x) = 11-x²

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Q: Use the first derivatives test to find the local exterma of f(x) =x3-12x on R

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Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

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Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

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Q: Find the derivative of the function by the limit process. f(x)=x2+x-1

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Q: Find the derivative by the limit process. f(x) = 15 – x²

A: Givenf(x)=15-x2Step -1From the definition of derivativef'(x)=lim∆x→0f(x+∆x)-f(x)∆x

Q: 4. If f(x) = sin x, show that f(2.x) = 2f(x)f(-x) %3D

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Q: Find the derivative of the function by the limit process. f(x) = x3 − 2x + 1

A: Given function is fx=x3-2x+1. From the definition of derivative, we have f'x=limh→0fx+h-fxh Using…

Q: 1 Use the limit definition of the derivative to find f'(x) if f (x)= 10x

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Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

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Q: 5)Let f ( x ) =3x4 + 4x3 Find the derivative. b)Find the critical numbers.

A: Given problem:- 5)Let f ( x ) =3x4 + 4x3   a) Find the derivative.   b) Find the critical numbers.

Q: Use the definition of derivative to compute f '(0). e-1/x if x * 0 if x - 0 f(x) f '(0) -

A: The definition of the derivative is given by: f'(x)=limh→0f(x+h)-f(x)h⇒f'(0)=limh→0f(h)-f(0)h  ...…

Q: Consider the function f(x) whose second derivative is f''(x)=2x+7sin(x). If f(0)=3 and f'(0)=3, what…

A: to find f'(x) integrate the given function c=integrating constant. Then plug x=0 and f'(0)=3 and…

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.