Find the domain of the function f(x) = ln(6 - x).

Q: Factor completely, or state that the polynomial is prime.: x3 + 3x2 - 25x - 75

A: To factorise the polynomial x3+3 x2-25x-75

Q: The volume of a cylinder with a radius of 5 inches is increasing at a rate of 36 ë in³ / min. How fa...

A: this question is solving with the help of implicit differentiation with respect to time  because hei...

Q: Find an equation of the tangent line to the graph at the given point.

A: The equation of the given graph: x23+y23=5

Q: Solve this initial value problem.

A: detailed solution is given below  

Q: 53.5 x 0.41 2.2     65.2 / 12 2.3     25.825 - 3.86 2.4     41.0 + 9.135 2.5    694.2 x 0.2

A: Given 53.5 x 0.41  = ?   65.2 / 12 = ?   25.825 - 3.86  = ?   41.0 + 9.135  = ?    694.2 x 0.2  = ? 

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

A: we have to determine if the series ∑k=2∞k+1-kk2-k converge or diverge   

Q: If f(x) = cos(2x), then f" Blank 1 4

A:

Q: Converges conditionally

A: According to the question, we have to define the term 'Converge conditionally'. The term Converge co...

Q: Tangent lines Find an equation of the line tangent to each of the following curves at the given poin...

A:

Q: Use l’Hôpital’s Rule to find the limits

A: If on substituting , one will get 00or ∞∞ form, one will use L-Hospital's rule, where one need to di...

Q: c) The following "theorem" is not quite true as stated: 1 Flawed "Theorem": arccot r = arctan- Fake ...

A:  

Q: Find the center, foci, vertices, and eccentricity of the ellipse, and sketch its graph. (x + 2)2 + (...

A:

Q: Find the limits

A: Given: The limit is limx→∞x+9-x+4.   Apply the limits. limx→∞x+9-x+4=∞-∞

Q: In Exercises 24-29, find the centroid of the region lying between thegraphs of the functions over th...

A: Given: y=ln(x) , y=x-1, 1,3

Q: How to do a

A: Given integral is, ∫0a∫0a2-x2dydx(1+x2+y2)3/2

Q: Solve this differential equation.

A:

Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning. A mo...

A: To determine whether the given statement makes sense or not

Q: Computing cross products Find the cross products u × v and v × u for the following vectors u and v ....

A: Consider the vector, u=2i-10j+15k,    v=0.5i+j-0.6k

Q: Use synthetic division to find the quotient and the remainder. (* +x - 1) +(x-3)

A:

Q: Consider f(x, y) = x³ + 2ry + y. Compute the following: (b)

A: Answer and explanation is given below.. Simply do partial derivative with respect to x and y.

Q: A 6000 -seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each pr...

A: Let x is the number of the first ticket ( $24 )  y is the number of the second ticket ( $40 )    A/Q...

Q: Below is a graph of y = f(x): %3D 3. 1 -1 -2 -3 1 2 3 45 6 7 8 Use this to compute 2. f(x)dx

A: given graph is now , we have to compute  ∫02f(t) dt

Q: Prove the shown?

A: we have been given limh→0sin hh=1 and limh→0cos h-1h=0 we have to use the limits to find the derivat...

Q: group of patients aff ients they note that population. The p mbers. Find the pa Use the separating

A: Let the size of the population be Pt where t=number of days after the initial breakdown. dPdt=kP dPd...

Q: The following function is positive and negative on the given interval.   ​f(x)=sin2x​; {0,(3π)/4}  ...

A:

Q: Find an equation of the inverse relation for the following relation. y= 3x-9 The equation of the inv...

A: Consider the given equation y=3x-9.  

Q: The radius r of a sphere is increasing at a rate of 1/8 inches per minute. Find the rate of change o...

A:

Q: Use the definitions of the hyperbolic functions to find eachof the following limits. limit x appraoa...

A: Here coshx=ex+e-x2 then sechx=1coshx=2ex+e-x.

Q: ing "theorem is not quite true as stated: Flawed "Theorem": arccot r 1 = arctan Fake "Proof": = arcc...

A: Given, we have to prove arccot x = arc tan1x

Q: Given r(t) = ⟨t, t2, t3⟩, find v(t) and a(t).

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) - 2) xp

A:

Q: Use the Product Rule or the Quotient Rule to find the derivative of the function y = sin x/x4

A: ddxxn=n xn-1 Quotient rule f(x)g(x)'=f'(x)g(x)-g'(x)f(x)g(x)2    

Q: A fly lands on one wall of a room. The lower-left corner of the wall is selected as the origin of a ...

A: The fly is located at the point having coordinates 2.10, 0.80. a). The distance from origin to 2.10,...

Q: Use the derivative ƒ' to determine the x-coordinate of the local maxima and minima of ƒ, and the int...

A: f'x=16x+1x-22x-3 Substitute the above derivative to zero. f'x=016x+1x-22x-3=0x=-1,3,2multiplicity 2 ...

Q: Prove that

A: Given:d2ndx2nsinx=-1n sinxd2ndx2ncosx=-1n cosx

Q: sin no 73. Investigate lim numerically for several positive integer values of n. Then guess the valu...

A: Given: The limit is limθ→0sinnθθ.   For n = 1. limθ→0sinθθ=sin00=00   Apply L'Hospital rule. limθ→0s...

Q: Graph the solution set of the system y > 2x - 3, y < -x + 6 of inequalities or indicate that t...

A: y>2x-3y<-x+6

Q: In the equation y =x³ - 3x² -24x + 6 the minimum point is said to be

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.