Find the length of the curve e +1 y = In a < x < b, a > 0. %3D e# – 1

Q: Use synthetic division to divide x3 - 7x - 6 by x + 2.

A: Divide x3-7x-6x+2 using synthetic division.

Q: Write the definition of the definite integral of a function from a to b. (b) What is the geometric i...

A: Definition of definite integral Geometric interpretation of f(x) for f(x)&gt;0 

Q: Write the equation in its equivalent exponential form. Solve, a. 3 = log7 x b. 2 = logb 25

A: Given that: The equations , a. 3 = log 7 x b . 2 = log b 25 

Q: By natural increase, a city whose population is40000 doubles in 50 years. There is a net additionof ...

A:

Q: Find csc π/4, sec π/4, and cot π/4.

A: Find the value of cscπ4.

Q: Are the addition formulas and double-angle formulas similar?

A: Solution:-  The question is  Are the addition formulas and double-angle formulas similar?  

Q: Get a particular solution

A: Explanation and Solution is given below....

Q: Prove the limit statements

A: Given;               limx→-3x2-9x+3=-6 Prove the limit statements limx→-3x2-9x+3=-6

Q: find all possible functions with the givenderivative. y' = 4x - 1/√x

A: Giveny'=4x-1x

Q: Describe the type of indeterminate form (if any) that is obtained by direct substitution. (a) Evalua...

A: limx→∞1+x1x By applying the limit, we get limx→∞1+x1x=1+∞1∞=∞0 a). limx→∞1+x1x=elnlimx→∞1+x1x      ∵...

Q: Find the value of the constant m that makes the following function continuous on (-00, 00). MI – 17 ...

A: Given that, fx=mx-17         if x&lt;-9x2+2x-8    if  x⩾-9 A function f is continuous at a point x=a...

Q: Designing a logistic model Wildlife biologists observe a prairie dogcommunity for several years. Whe...

A: Logistic relation of the formy=c1+abxc=carrying capacity, limit to the growth

Q: A point is moving along the graph of a given function such that dx/dt is 3 centimeters per second. F...

A: We have to find dydt for difference values of x where, y=3x2+2 and dxdt=3. We know formula of differ...

Q: Graph the solution set of the system of inequalities or indicate that the system has no solution.

A: Graph the solution set of the system of inequalities or indicate that the system has no solution. x2...

Q: Find the lengths of the sides of the triangle with the indicated vertices (0, 0, 4), (2, 6, 7), (6, ...

A: we have been given the vertices of the triangle (0, 0, 4), (2, 6, 7), (6, 4, −8). we have to determi...

Q: 12. A gallon of milk is slowly leaking inside your refrigerator. The number of ounces in the contain...

A: Given a gallon of milk is leaking inside the refrigerator. The number of ounces in the container lef...

Q: Simplify the radical expressions if possible. ∛ 9 . ∛6

A: The given expression is 93·63

Q: When a plane flies with the wind, it can travel 1600 kilometers in 2 hours. When the plane flies in ...

A: Given: When a plane flies with the wind, it can travel 1600 kilometers in 2 hours. When the plane fl...

Q: Use the graph of the rational function in the figure given (see attached) to complete the statement ...

A: Use the graph of the rational function in the figure given (see attached) to complete the statement ...

Q: Find the inverse function of f over the given interval. Describe the relationship between the graphs...

A:

Q: Trigonometric integrals Evaluate the following integrals.

A: To evaluate the given integral , ∫0π6tan52x sec2x dx Solution: The given integral can be simplified ...

Q: Give the center and radius of the circle described by the equation (x + 2)2 + y2 = 16 , and graph th...

A: we have been given the equation of circle  (x + 2)2 + y2 = 16  we have to find the center and radius...

Q: Choose a convenient order When converted to an iterated integral, the following double integrals are...

A: Consider the given double integral, ∬RycosxydA  where R=x,y: 0≤x≤1, 0≤y≤π3 now, it is easier to take...

Q: Insert either &lt; or &gt; in the blank area between the numbers to make the statement true, √2 ….. ...

A:

Q: we have the following differential equation y``+3y`=12x-5 you can find particulate solution yp throu...

A:

Q: Solve absolute value inequality. |5x - 2 | &gt; 13

A: We have to solve the absolute value inequality: 5x-2&gt;13 Case first: When 5x-2&gt;0⇒x&gt;25 then 5...

Q: Find the inverse ƒ-11x2 of each function (on the given interval, if specified). ƒ1x2= e2x+6

A: The given function is fx=e2x+6. To find the inverse of the given function. Solution: Let us take y t...

Q: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what r...

A: Given: S the surface area of the cube, x the length of the cube and the length x of the cube decreas...

Q: Are all polynomials rational functions? Are all algebraic functions polynomials?

A: It is known that all polynomials are not rational functions.  Example: Consider the function fx=π. T...

Q: Find the domain and sketch the graph of the function.

A: Find the domain and sketch the graph of the function.

Q: Express interval in set-builder notation and graph the interval on a number line. (- ∞, 3.5]

A: Express interval in set-builder notation and graph the interval on a number line. (- ∞, 3.5]

Q: Each integral represents the volume of a solid.Describe the solid.

A: Shell method: The volume of a solid generated by revolving the region bounded by y = f(x)  and the x...

Q: Find general solutions of the differential equation  4xy^2+y'=5x^4y^2

A: the given differential equation is: 4xy2+y'=5x4y2   the given differential equation can be written a...

Q: ■ Find dy /dx  by implicit differentiation 2x3 + x 2  y - x y 3 = 2

A: 2x3+x2y-xy3=2

Q: Integer

A:

Q: find the radius of curvature of the curve r = a sin n theta at the pole in polar form

A: Consider the polar curve: r=asinnθ Radius of curvature (R) of polar curve r=f(θ) is  R=r2+r123/2r2+2...

Q: Show that the normal line at any point on the circle x2 + y2 = r2 passes through the origin

A: Assume that we have the circle of equation x2+y2=r2 and we want to get the normal equation at x0,y0....