According to the graph of f(x) given below, f(x)– 2 (a) Is lim positive? ("yes" or "no") [a] (b) lim h+0 f(1+h)– 1 = [b] 3 -2 -1 3 --

Q: 1- Find the limits: lim V - 1 メ→ x-1 а. 2x3 b. lim x- 00 3(x-2)2 2x3 c. lim x2 3(x-2)2 x+1 d. lim…

A: Consider the limits  a.limx→1x−1x−1b.limx→∞2x33x−22c.limx→22x33x−22d.limx→3x+13−x2

Q: Find the lim f(x), if it exist where 3x X 5 f(x) = 2x-1

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Q: Sketch the graph of if x 2 f(x) = if and use it to determine the values a for which lim f(x)…

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Q: (-금x+ 2, x 0 exist? If yes, give its value. If not, why?

A:

Q: 2. By drawing a graph illustrate an example of a function f(x) such that it satisfies these three…

A: Topic = Functions

Q: The graphs of f(x) and g(x) meet at x = 1. Evaluate lim g(x) x-1/(x)

A: Given: the graph of f(x) and g(x) meet at x=1

Q: Find the one-sided limits of f (x). - 2x + 7 if x < -3 f(x) x + 4 x + 3 %3D if x 2 -3 Step 2 of 2:…

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Q: _15. What is lim f(x)? X-4 A. 0 В.1 С.2 D. Does Not Exist

A: Given: Following graph is given. To Find: 15. limx→4fx=?

Q: sketch the graph of a function with the given limits.

A: the given limits are:

Q: Consider the graph of y = f(x). 4- -8 -7 -6 -5 -4 -3 -2 -1O 2 3 5 -2 For infinite limits, use 00 = 0…

A: As per our guidelines we are supposed to answer only first three parts. kindly repost others part as…

Q: Consider the function Pue au Marka 1- x2, x1 f(x) = 2, %3D X = 1 Graph the function f(x). Find…

A: (Since it is not mentioned which question to solve and question 4 part 2 is not clear so Solving the…

Q: V2x + 10 + Vx² – 5x + 10 lim - X→-1 x² + 1

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Q: Sketch the graph of a function with the given limits.

A: Given the function with the limits.

Q: 4. Is it possible that there exists some function g(x) and some constant L such that lim g(x) = lim…

A: First we need to understand definition of limit:

Q: Determine the infinite limit. a) lim -3- (x – 3)5 b) x – 1 lim 0 x(x + 2) c) x² – 2x lim a-2- x? –…

A: (a) The given limit is: limx→3-xx-35 To find the value of the limit.

Q: 1. Find a) lim x3 3-x b) lim- x3* 3-x ,c) lim- x+3 3-x

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

Q: Let ƒ(x) = (x^2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01,…

A: Consider the given function:

Q: a. Using the Sandwich Theorem to find: lim f (x) If v5 – 2x2 <f(x)< V5-

A:

Q: 1- Find the limits: VI- lim X X-1 а. 2x3 b. lim x→ 00 3(x-2)2 2x3 с. lim x2 3(x-2)² x+1 d. lim X-3…

A: Given: )

Q: The function f is continuous for all real numbers. If lim f(x) = 0, then what is lim xe-2x)? x-2 x-1

A: The function f is continuous for all real numbers  If limx→2f(x)=0then if we put x=2t then…

Q: 1. Let f(x) = lim 1-0 7x3 + 3x² °

A: The given function is: f(x)=limx→0x27x3+3x2

Q: Find a number b such that lim- .2. x²-4 =2 x-b x-x -2

A:

Q: 22. If lim f(x) = 18 and lim g(x) = -1.5, find the lim %3D %3D x-a L4g(x). xa А. 6 -3 С. -1 D. -7 В.

A: 22) If limx→afx=18 and limx→agx=-1.5 , find the limx→afx4gx

Q: x*-a* If lim (108 * T'), find the value of "a". х-а х-а

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Q: the graph of an example of a functionf that satisfies all of the given conditions. 15.) lim f(x) =…

A: We have to solve given problems: We

Q: Sketch a possible graph of a function that satisfies the conditions below. (0) 0, lim f(x) - 1; lim…

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Q: a) Find the limits: 1- lim- X-1x-x 2- lím 0 V+4-2 5x 3- lim

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Q: Consider the graph of a function shown here, and use it to evaluate the limits: -5- 5 -5- lim f(x) :…

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Q: When the function f(x) satisfies f(1) =1,f'(1)= 3 obtain a value of lim/ (2)" -1 x→1 x² – 1

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Q: Find the value of * lim - 1 - 1 1 +x

A: Let us take f(x)=x11+x-1. Then we have to find limx→0f(x).

Q: what is the lim x->0  f(x)-f(0)/x^2 if f(x)=2x^2+1?

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Q: If f(x) = 3x2 - 4x +1 and g(x) = x² + 2x - 3, then what is lim 9X, g(x). X-1 f(x)

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Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

Q: . Is it possible that f(2) = 5 but limx→2 f(x) = 7? If so, what kind of function can satisfy this?

A:

Q: Find. 1) a. lim f(x) and b. lim f(x). 3- 4-

A: Answer and explanation is given below..

Q: e2h-1 if f'(a) lim-0 what is f(r) and what is a? h

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Q: Find the limits as x - 0o and as x - -00. y = f(x) = (3 – x)(1 + x)?(1 – x)4 lim f(x) = lim f(x) = X…

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Q: X # 1 f(x) = 0, x = 1.

A: Solution is given as below:

Q: x-2 51. lim x-1x-1

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Q: 1 1 Find the limit lim *+5 8 x→3 x-3

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Q: 1. Sketch a graph of a function f(x) with the following properties: f(-2) = 0, ƒ(2) = 0, lim_f(x) =…

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Q: 10. lim 2-と is A. -1

A: we have to find the value of the given  limit  lim    x→-∞2-x2x

Q: B. Evaluate the limit of a function using the co indeterminate forms. 6x2-7x-3 1. lim 2х-3 X- V2x-…

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Q: 1. Find a) lim x3 3-x b) lim x+3* 3-x c) lim- x+33-x d) the vertical asymptote of f(x) =- 3-x

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: 1. Find a) lim b) lim x→3* 3-x c) lim=-, d) the vertical asymptote of f(x)=- x→33-x 3-x

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Q: Sketch the graph of a function f such that: limf(x)=0 X-7

A: We take a function  f(x)= 1/(x-7)

Q: Given that lim f(x) = 4 and lim g(x) = -2. Find the value of x-2 x-2 lim 4f(x) + x-2 [g(x)]³ ) 2

A: we find the value of given limit

Q: Find all values c such that lim x-2 2c²x 5c +1 x²-3x + 2 - exists. (a real number)

A: We say a limit exists if right hand limit and left hand limits are same. We have…

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.