Find dy/dx at x = 1 by first using laws of the logarithm function. %3D y = In(x* dy (2x+1)³) - In( tanx cotx) %3D (Enter the numerical value in the blank) %3D dx

Q: Sketch the curve represented by the parametric equations x = t − 3,                  y = t/(t − 3) (...

A: Given: x=t-3                                                  ..1y=tt-3                             ...

Q: Suppose the value of timber (already planted on some given land) is the following increasing functio...

A: Given: Function of time V=1000(2)t. Interest rate is 6%. let the present value be A. Therefore Acc...

Q: Please solve it

A:

Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨4, 5⟩

A: we have to find a and b such that v=au+bw where u=1,2 and w=1,-1 and v=4,5. the given vectors are: u...

Q: A box with an open top has vertical sides, a square bottom and a volume of 4 cubic meters. If the bo...

A: Given that x represents the length of the sides of the squares base and h the height of the open box...

Q: At what value of x does the function f(x) =3 x-Vx change from decreasing to increasing? 1/9 1/8 1/3 ...

A:

Q: Consider the function f(x) = x' – 15x2 + 73x - 115 defined on the interval [4, 6]. Verify the Mean V...

A:

Q: describe the given set with a single equation orwith a pair of equations. The plane through the poin...

A: Plane passing through the point 3, -1, 2 and perpendicular to the z-axis. Since the plane is perpend...

Q: Find the exponential function y = Cekt that passes through the two given points.

A:

Q: Find the derivatives of the functions y = (1 + x2) etan-1 x

A: Product rule (uv)'=u'v+uv' ddxxn=n xn-1ddxex=exddxtan-1x=11+x2

Q: I need help with the following. Thanks

A:  Since you have asked multiple questions in single request so we  will be answering only first quest...

Q: Determine whether the statement is true or false. If it is false, explain why or give an example tha...

A: Consider the given statement If limx→cfx=L   and   fc=L, then f(x) is continuous at 

Q: Solve the triangle B = 107°, C = 30°, c = 126. Round lengths to the nearest tenth and angle measures...

A: Given that the triangle,   B = 107°, C = 30°, c = 126   To sketch the triangle,

Q: Solve the logarithmic equation for x. (a) log(2x) = 3 (b) log(x + 1) + log 2 = log(5x) (c) 5 In(3 – ...

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want an...

Q: Given that f"(x) = cos(x), f'(a/2) = 13 and f(t/2) = 14, find: %3D %3D f'(x) = f(x) =

A:

Q: Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain...

A: Let the given function be f(x) - f(x) = xx2+4x2-4f(x) = xx2+4x2-22f(x) = xx2+4x+2x-2We can expand or...

Q: 23-5.7

A:

Q: A spherical balloon is being inflated so that the volume is increasing at the rate of 5 cubic feet p...

A: V=43πr3dVdt=5 cubic feet per minuteradius, r=6 feetFormuladdxxn=n xn-1

Q: Use the matrices below to perform matrix multiplication. -4 11 4 7 B = 6. 4 9 0 12 8 -10 3

A:

Q: You know the Excelsior must achieve 30,000 mph to reach escape velocity. Therocket’s engines are sta...

A: The acceleration of the rocket is, anet=10t-32 Calculate the velocity of the rocket from the above e...

Q: dx The coordinates of a particle in the metric xy-plane are differentiable functions of time t with ...

A: Given:          dxdt=-5 m/sdydt=-2 m/s Distance of a point (x,y) and the origin is calculate by;    ...

Q: If sin θ = a and cos θ = b, represent each of the following in terms of a and b. Solve, a. sin(-θ) +...

A: sin(-θ)=-sinθcos(-θ)= cos θtan θ=sinθcos θsecθ=1cos θ

Q: Computer algebra systems sometimes need a helping handfrom human beings. Try to evaluate integral  (...

A: To evaluate∫1+lnx1+xlnx2dx  ........1

Q: The limit represents f′(c) for a function f and a number c. Find f and c.

A: By the definition of derivative for a function f at a point x=a is f'a=lim∆x→0fa+∆x-fa∆x We have giv...

Q: Find the shown limit?

A:

Q: Define Sturm-Liouville Eigenvalue Problem for Inner Product Space ?

A:

Q: Estimate the error if cossqrtt is approximated by 1-t/2+t^2/4!-t^3/6! in the integral  cos((sqrt)t)d...

A: For the given  Cos t = 1-t2+t24!-t36!+.... error is estimated as shown below   

Q: For the following, set up an integral that will compute the area between the curves. Show all necess...

A:

Q: Find the indefinite integral ∫ 1 / (25 + 4x2) dx

A: ∫11+x2dx=tan-19x)+C

Q: Show using Definition 4.3.1(Continuity) that if c is an isolated point ofA ⊆ R, then f : A → R is co...

A: If c∈A⊆ R is an isolated point of A ⊆ R. To prove  f : A → R is continuous at c. Let ∈>0 , Since ...

Q: 11.please show me all steps

A:

Q: Use the graph of f to determine the following. Where applicable, use interval notation : a. the doma...

A:

Q: Find the following sum:

A:

Q: Find the limit as k approaches infinity of 1 + 1 10k 10 1 2 e

A: Given, limk→∞1+110k10k    We have to find the value of the above limit.  

Q: Verify the following indefinite integral by differentiation.

A: Given: ∫xdxx2-12=-12x2-1+c for verifying given integral, we differentiate R.H.S. with respect to x  

Q: A jet airplane reaches 630/kmh on a certain flight. How long does it take to cover 477m? Set the mat...

A: given velocity(v) = 630kmhvelocity in ms cam be written asv=630×10003600v=175ms

Q: 21-5.7

A: Given: y=sin(x)1+cos(x)

Q: Set up (but do not integrate) the integral used to find the area between the curves y = 8+4x-x^2y=8+...

A: We first draw the functions using a graphing calculator.    

Q: Use the formula for the general term (the nth term) of a geometric sequence , to find the indicated ...

A: a1=8000, r=-12

Q: 5. Determine the equation of the tangent line for y = sech(ln x) + tan¬1(x²) tangent at x = e* . A. ...

A: Consider the given equation y=sechlnx+tan-1x2 The value of function at x = e4 is y=sechlne4+tan-1e42...

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: