Prove that the function defined by defines a one-to-one correspondence from (0, 1) to R.

Q: 1. Given a supply function S(x) = 300 +15x find the average price in dollars over a supply interval ...

A: Given,

Q: (a) Show that e>1+ x if x> 0. [Hint: Show that f(x) = e* – (1 + x) is increasing for x> 0.] (b) Dedu...

A: If x≥0 as exp is increase we have ex≥1. they by means value theorem there exist c∈0,x such that     ...

Q: Use the given measurement a = 400, b = 300 to solve the following triangle. Round lengths of sides t...

A: Given: a = 400, b = 300  According to sine rule  bsin θ=asin 2θ

Q: Denominator may reduce the fraction to one whose denominator is no longer zero.True or false?

A: Given:Denominator may reduce the fraction to one whose denominator isno longer zero

Q: Evaluate the definite integral. Use a graphing utility to verify your result

A: Given integral ∫45x2x-6dx Substitute  u=2x-6 Upper limit at x=5 is 2. Lower limit at x= is 2 =∫22u2+...

Q: Evaluate the following integrals.

A:

Q: Find the volume of the solid obtained by rotating theregion bounded by the given curves about the sp...

A:

Q: Problem 13. Let the functions f, g, and h be defined as follows: f(x) = { x sin(1/x), for x 0 for x=...

A: The function f(x) should be differentiable at a point f(a)  if and only if, 1)f(a) exist2)Ltx→af(x) ...

Q: Solve  ∫1/(324-x^2)dx

A:

Q: Find the x-coordinate of each point of inflection of the graphof g on the open interval (-3, 4).

A: Given, we know that, g(x)=∫1xf(t)dt

Q: A modernistic painting consists of triangles, rectangles, and pentagons, all drawn so as to not over...

A: From given information consider the equations, x+y+z=40              ...13x+4y+5z=153     ...22y+5z=...

Q: Evaluate the following integrals.

A: We have  I=∫1e1dxxln2x+2lnx+2                         ⋯⋯(1) Let  lnx=u1xdx=du       and limits  u→-1...

Q: A person has two parents, four grandparents, eight great-grandparents, and so on. What is the total ...

A: The person has two parents, four grandparents, eight great-grandparents, and so on. This makes the s...

Q: State the name of the property illustrated.6 + (-4) = (-4) + 6

A: The expression is given as 6+(-4)=(-4)+6Now the objective is to state the name of the property of th...

Q: Simplify the expression shown.

A: Given: ft=ddt∫1t3dxx-∫t213dxx for finding ft, we use fundamental theorem of calculus according to fu...

Q: When graphing the solutions of an inequality, what does a parenthesis signify? What does a square br...

A: When graphing the solutions of an inequality, what does a parenthesis signify? What does a square br...

Q: Find the area of the largest rectangle that can be inscribed in asemicircle of radius r

A:

Q: Determine whether the following series converge. Justify your answers.

A: Given: ∑k=1∞ 7k+11k11k Determine whether the following series converge. Now rewrite the given series...

Q: 10. A stone is dropped from a building 256 ft high. How long it takes the stone to reach the ground?...

A: As per given information: Height of building: h=256ft. a) As the formula: As stone is dropped so ini...

Q: Evaluate dy/dx @ the given point y^5-4=x^5-2y  @ (-1,1)

A: The given equation is  y5 - 4 = x5 - 2y We know that (d/dx) xn = nxn-1

Q: Perform the indicated operations. Write the resulting polynomial in standard form and indicate its d...

A: To solve the expression:17x3-5x2+4x-3-5x3-9x2-8x+11 Solving the expression: 17x3-5x2+4x-3-5x3-9x2-8x...

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the R...

A: To determine the convergence or divergence of the series ∑n=1∞1+13n-n2

Q: Answer the following questions about the functions whose derivativesare given:a. What are the critic...

A:

Q: The time, t, in weeks, needed for the population of fireflies in a field to reach p individual is gi...

A: Consider the given function tp=45ln10,00018000-p

Q: Begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to gra...

A: Domain of function fx=x is x≥0. Graph of function fx=x x 4 1 0 9 16 fx 2 1 0 3 4

Q: A simplified polynomial that has three terms is called a/an___________.

A: A simplified polynomial that has three terms is called a/an................

Q: Use the Integral Test to determine whether the infinite series is convergent. 00 Σ 1 n² + 25 n=5 Fil...

A: To use integral test to determine the infinite series is convergent  ∑n=5∞1n2+25

Q: Use logarithmic differentiation to find dy/dx.

A: ln(mn)=ln(m)+ln(n)lnmn=ln(m)-ln(n)ddxln(x)=1x

Q: The rate of change of y is proportional to y. When t = 0, y = 2, and when t = 2, y = 4. What is the ...

A: Given that rate of change of y is proportional to y that is, dydt=ky        ...(1)

Q: Multiply: (7x - 5)(4x - 3).

A: Given:7x-54x-3

Q: 8. If the radius and height of a cone grow 1.8% and 2.0% from its original value, respectively, calc...

A: The volume of cone(V), with radius (r) and height (h), is given by, V=13πr2h Substitute h=2r to get ...

Q: In Exercises 27–28, the the following limit could be helpful: lim + = e. 28. Does (2n)! converge or ...

A: We have given series  ∑n=1∞2n!nn We will use here ratio test. Let ∑n=1∞an=∑n=1∞2n!nn Then, an=2n!nna...

Q: Use any method to evaluate the integrals. Mostwill require trigonometric substitutions, but some can...

A: The given integral is: ∫x24+x2dx To evaluate this integral, substitute x=2 tant .....(1) Differentia...

Q: What is the derivative of r(t) = ⟨ƒ(t), g(t), h(t)⟩?

A: we have the vector r(t) = ⟨ƒ(t), g(t), h(t)⟩   r′(t) is the derivative of the vector r(t)  The vecto...