you can draw a square inside another square by placing each vertex of the inner square on one side of the outer square. The large square in the diagram has side length 10 units  a) determine the area of the inscribed square as a function of x b) determine the domain and range of this area function  c) determine the perimiter of the inscribed square as a function of x d) determine the domain and range of this perimiter function

Q: express the set of numbers x satisfying the given condition as an interval.       I x+ 7 I < 2

A: Given: x+7<2 We know that solution of inequalityx+a<b is given by -b<x+a<b

Q: Use the given graphs of f and g to evaluate the expression. ---- . -2 (gof)(3) = %3D 654 m2

A:

Q: Use interval notation to represent all values of x satisfying the given condition. y = 7 -  | x/2 +…

A:

Q: -=f"(() is The degree of precision of a quadrature formula whose error term is :-

A: To find- The degree of precision of a quadrature formula whose error term is: -h336f''ξ is

Q: Let H=Span{1+2t,1-2t°}, then dim H=

A: There are two vectors. We need to find out if they are linearly independent. Consider a(1 + 2t) +…

Q: 13 Give the six circular function of 4.

A: To find: The six circular function of 13π4 (θ=13π4)

Q: Use interval notation to represent all values of x satisfying the given condition. y = 1 - (x + 3) +…

A: y=1-x+3+2xy is atleast 4 i.ey≥41-x+3+2x≥41-x-3+2x≥4

Q: ketch represents f(x) = x² + x – 6 and g(x) = -x - 3 M If MN = 3, calculate the possible length(s)…

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A:

Q: Find the supremum and infimum of the set x € R:x = +(-1)" ,n e N} + (-1)" ,n e N}

A:

Q: Show that the interval [a,b] is complete

A: Given

Q: Find all real numbers  x such that  x^6−3x^3−18=0. Give your answers in increasing order.

A:

Q: ■ Find a formula for the described function and state itsdomain.47. A rectangle has perimeter 20 m.…

A:

Q: A cubic function can have at most, how many unique zeros? O 3 O 1 O 2 6.

A: As we know that a cubic function is degree 3 polynomial function.

Q: Does the Nearest Point Theorem in R imply that there is a strictly positive real number nearest…

A: The statement of the Nearest Point Theorem is as follows: "Let A be a non-empty closed convex set in…

Q: Q3/ By using definition, proof that cot x = - csc² x. xp

A:

Q: a) Solve for x in the following questior 7-x = 1 %3D

A:

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A:

Q: Given two nonnegative numbers a and b such that a + b = 4, what is the difference between the…

A: Given ,          a+b=4             b=4-aGiven expression=a2b288   fa=a24-a288…

Q: The degree of precision of a quadrature formula whose error term is: is ww

A:

Q: Find the range of the possible of x

A:

Q: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…

A: solution is given below:

Q: Given positive real numbers x and b such that b + 1, y = log, x is the is equivalent to b' = x.…

A:

Q: A) Find the domain and range f the fnetion メーし メ+2 ユーメ-

A: Explanation of the solution is given below...

Q: 13. Let P be the perimeter of a rectangular fence. Prove that the shape that encloses the maximum…

A:

Q: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…

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Q: Use interval notation to represent all values of x satisfying the given condition. y = 8 -  | 5x + 3…

A: The function is y=8-5x+3. The condition is y≥6.   Thus, 8-5x+3≥6.   Simplify. 8-5x+3-8≥6-8…

Q: Let G be a vertical stretch by a factor of 2, followed by a translation 2 units up of the graph of…

A: First determine the transformation 1 for vertical stretch 2. f(x)=x+3For vertical stretch by factor…

Q: The function 3 satisfies the hypotnes Find all values of c that satisfy the conclusion of the…

A: Topic:- application of derivatives

Q: The degree of precision of the following quadrature rule: 1 12

A:

Q: Find the domn sketch the araph of the trigonametvic function vange , amplitede, peried, and

A:

Q: Let x be a real number. Prove that there is a positive integer n such that the distance between nx…

A: Let x be a real number  To prove there is a positive integer n such that the distanc between nx and…

Q: x-4 f(x) = In %3D x² – 5x + 6)

A: Given:  f(x)= ln x-4x2-5x+6⇒ f(x) =…

Q: Show that : [x+y] > [x] + [Y] for any real numbers x and y

A: Introduction: The greatest integer function is a significant number theoretic function. Every real…

Q: 14. A 2x + 17 25 112 B 133 25 D 39

A: The converse of the Hinge theorem states that when two triangles have two congruent sides, then the…

Q: The range of the function, whose graph is shown above, is . Set braces {} required. Use commas. No…

A: Recall:  In graph, the range consist of all the possible output values shown on the y-axis.

Q: a) In the set of real numbers A = {x | | x - 2 | > 1, x E IR} cluster is given. Accordingly, express…

A: 1) A) The given set is: A={x||x-2|>1,x∈ℝ} Here,  |x-2|>1⇒x-2>1 or x-2<-1⇒x>3 or…

Q: Using the Intermediate Value Theorem and a calculator, find an interval of length 0.01 that contains…

A: Let's find.

Q: Let a, x, and y be real numbers and let e > 0. Suppose that |x-al < e and y-al <e Use the Triangle…

A: Given that, a, x, and y be real numbers and let ε &gt; 0Also,x-a&lt;εand y-a&lt;εWe know…

Q: e and F are sets of real numbers defined as follows. E={v| v7} Write EUF and ENF using interval…

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Q: Point E is on line segment DF. Given DE = 2x, EF = 2x - 6, and DF 3x + 5, determine the numerical…

A: Solution : The correct answer is 16 .  The length of EF = 16

Q: Use interval notation to represent all values of x satisfying the given conditions: y = 7 - lx/2 +…

A: y=7-x2+2

Q: Use interval notation to represent all values of x satisfying the given condition. y = 2x - 11 + 3(x…

A: Use interval notation to represent all values of x satisfying the given condition. y = 2x - 11 + 3(x…

Q: A quadratc function has root af|E and passes throwgh the pDint (1,-9) Find the equations of the…

A: Introduction: The standard form of the quadratic function is given by, f(x)=a(x-h)2+k

Q: The domain of y = cot x is all real numbers such that ________.

A: We know that, cotx=cosxsinx Here cotx is defined if and only if sinx≠0.

Q: Use analytical and/or graphical methods to determine the largest possible sets of points on which…

A: Use analytical and/or graphical methods to determine the largest possible sets of points on which…

Q: Quadrilateral BCDE is dilated with scale factor and - center A onto quadrilateral FGHI.

A: NOTE- AS WE ARE ALLOWED TO ANSWER MAXIMUM THREE SUBPARTS OF ANY QUESTION. SO, I HAVE ANSWERED FIRST…

Q: Awadallah, Ahmad 2021 1 2 of 25 Which graph models the transformation of the quadratic parent…

A: Given  f(x)=x^2 g(x)=f(x-1)+4 i.e g(x)=(x-1)^2+4 Graph of f(x) is passing through origin.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.