fb) 2x -3 < 4x +3 < 2x+5

Q: Use logs and implicit differentiaton to prove (root(x))' = 0.5x^(-0.5)

A: Let y = √x Take log to the base e, i.e. natural log, i.e ln on both the sides, ln(y) = ln(√x) =…

Q: 1. Use the Intermediate Value Theorem to prove that the equation 3x - 4x² = 3 is solvable on the…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: A and Bare open and bounded.

A: For second one we can take any two open interval one of whose right end point ar same of the others…

Q: Find a point c satisfying the conclusion of the MVT for the func y(x) = 2e* on the interval [0, 5].…

A:

Q: 4. [5] Please find in interval notation the values of x for which this expression is real. Show…

A:

Q: branch of z1/5 that is not continuous and positive on the imaginary axis?

A:

Q: Show that R2 =

A: Then, V =Span(S), if every vector in V can be written as a linear combination of elements of S.

Q: 5. Use the Intermediate Value Theorem (IVT) to show that the equation below has a root in the…

A: Given that, The function is, f(x) = 2x3 + x2 + x + 3 = 0 interval is = (-2, 0) We have to prove by…

Q: 8. Use finite differences method to classify the following relations as linear, quadratic or…

A: In this question, the concept of the finite differences method is applied. Finite Difference Method…

Q: 1. Differentiate. Show your work to get credit. a) g(x) = x* In(2.x² +7) by using the product rule.

A: SInce multiple subparts are asked, I am ansering only first 3

Q: symmetri

A:

Q: 8. Is the set of functions f₁(x) = 3e³x and f₂(x) = -3e3³* independent? Show using the -3.x…

A: Given functions- f1x=3e3x  and  f2x=-3e-3x To show whether the given set of functions is independent…

Q: Show that the multiplicity of (x-1) is 1.

A:

Q: D if x,Y,2 inclepndent Variables and z function in X, Y which achieves the eguation find az…

A:

Q: Exampi r(x) = (/2x + 1 - x²)-1 %3D "(x) =

A: Given query is to find the derivative of the expression.

Q: Use metaphor/layman's term to describe that Q is dense in R

A:

Q: 14x'y What is the simplified form of 2

A: To write the simplified form of the given expression

Q: find the anti- deriva tive of the fun cticn: fcx) = 4 cSca cotx - Secx cot x

A: Derivative of function

Q: What is the minimum number of times you would expect f(x) 6 in the interval (0, 40? %3D

A: from the given table we cansay (As f(x) in continuoun everywhere)∃ x1∈ (0,10) such that,…

Q: Find abs. max 8 min f(xeg) = x²-3y² - 2x + 6y | on R: square which vertices Coc0)r (200] (2ィ2),(o/2)

A:

Q: | x(1 – x)193dx

A: Proceed as shown below

Q: 2) Find FCO), if it exits Punctien f(z) - 2 if x raticnal if x irraticnal

A:

Q: An arbitrary point x of 0.1 is chosen. Since it is known that x> = 5, what is the existence of x> =…

A: x is an arbitrary point of (0,1)  and x ≥0.5x≥78=0.8

Q: Write a V ation of the line below. 8- 6- 2- -8-7 -6 -54 3-21 2345 6 -2- 4. -5. -6- CO

A: Given the graph of line:

Q: Show that Rsta is Hausdorff.

A: Note that a topological space X,I is said to be Hausdorff if (and only if) for every distinct points…

Q: Questione Let R=7LO7L. Show that the palynomials (,0)x in R[x] has in finitely many roots.

A:

Q: Does S = {x² + 1,x² – 1, 2x – 1} span P2?

A: we know dimension of P2 is 3 so any set which span P2 must have at least 3 elements. here given set…

Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show…

A: We will find out the required value.

Q: 5. Show that Ax) = Inx² - 1- In/3, if f'(x)= and (2) = 0. x- 1 Justify your answer.

A: To show that f(x)=ln|x²-1|-ln√3

Q: and こ=< ,フ-<o,-1y. where %3D Pind マf(2)?

A:

Q: Show that 1 -2 = R³. span 3 1

A: In R^3 if three vectors are linearly independent then they span the whole space R^3.

Q: Find the averuge valuc of the function fcx)-4x4 on the interval [2,6],

A: Given : fx = 4x4

Q: Let f(æ) = Vr² – 5, g(x) = , h(x) = go((gof)+h(x)) at x=-1? Find - %3D 22-9

A:

Q: What is the domain of { (z,3z2- 5) Iz ER except 0}? All real numbers All negative numbers {x\x€R>0}…

A:

Q: 6. Prove from first principles (with ac- 6 argument ) that लेग ½ lim 7--1

A: 1x2+1-12=2-x2+12x2+1                               =2-x2+12x2+12+x2+1…

Q: Show that div (r x a) = 0

A:

Q: Show that the f(x)=x-(In x)^{x} =0, has at least one solution in the interval [4, 5].

A: There are more than one question. We will solve the first one. Given, f(x)=x-[ln(x)]x, we need to…

Q: 2. Using both a picture and words, explain the Squeeze Theorem.

A: Given : The Squeeze Theorem.

Q: Find two positive real numbers x and y such that they add to 123 and  x2y  is as large as possible.…

A: We have to find out x and y

Q: Itiple of 2} and B = {multipl %3D isible by 3} and B = {divisib

A: As per the bartleby guidelines for more than three parts only three has to be solved . Please upload…

Q: Find the value of K that make s the funtion fcx) Continus : x*+ 3K メニ2; %3D 2K-X > 2

A:

Q: Prove that y = e-3* (Acos 5x - Bsin 5x) + Cx; A, B and C are arbitrary constants will equalto y"(17x…

A: Given,            y =e-3xAcos 5x -Bsin 5x + Cx

Q: 7. Use the Intermediate Value Theorem (IVT) to show that there is a root of the equation In r = 3 –…

A: We can use intermidiate theorem in order to solve the given problem.

Q: hraj h(x) = 3x-2 x347

A:

Q: The algebraic translation of "x is no less than 7" is .

A: Given statement is "x is no less than 7:. To translate into algebraic form. Solution: Given that x…

Q: Use loparithmic differentietion to find derivetive! 2x3+3 :- 3. = (x)융 XG-9A

A:

Q: Use intermediate theorem to explain P [x] = x* – x' – 10 has a zero in [2, 3]

A: According to intermediate value theorem of a function f(x) is continuous on [a, b] and L is any…

Q: 3. Show that 5 x + 7 is a continuous fimction

A: Let, f(x) = 5x+7 be defined over R, the set of all real numbers. Choose an arbitrary point c in R.…

Q: Prove Formulas (1) - (9) Differentiate y = √3x². - 1 √5x = = (3x²)¹/³ – (5x)−¹/2

A: