Find the derivative of the following functions: 5. y = tanh 2x +coth 3x ans. y' = sech²2x – 2csch²3x 6. у %3D sinh? (3x? — 1) ans. y' = 6xsinh(6x² – 2) 7. f(z) = Arctan (sinh 6z) ans. f'(z) = 6 sech 6z

Q: Find the derivative of the function. f(x) = 4/5 4 + X f'(x) ||

A:

Q: In(n) Σ

A:

Q: 3(sin y– cos y)°dy cos y

A:

Q: Sketch the cardioid r = 3 cos 0 and find the coordinates of the points on the cardioid where the tan...

A:

Q: Using either permutation or combinations: Seven children are to be selected from a group of nine ch...

A: a)  As the Danylo and shuying are included . So now we have to select 5 children out of remaining 7 ...

Q: One of the methods discussed in Chapter 2 leads to a solution of the following first order different...

A:

Q: The integration expression sin(3ln(x)+ 4)cos(3In(x) + 4)dx must be transformed into using suitable c...

A:

Q: sin 8 ydy 8. 25+ sin* 4y 4.

A:

Q: /x + Vy = 4 find the first derivative %3D

A: We know that; The sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1   Given: x+y=4

Q: find f ′(x) for each function. f (x) = 8x4 + 9x2 – 1

A: The given function,        fx=8x4+9x2-1

Q: Solve the separable differential equation for u du ebu +9t dt Use the following initial condition: u...

A:

Q: 11. Determine three positive numbers x, y and z whose sum is 10 that produce a maximum value for the...

A: x,y and z be the three positive numbers whose sum is 10that produce a maximum value for x2yz

Q: Let f(x) = V43 – ¤ %3D The slope of the tangent line to the graph of f(x) at the point (7, 6) is The...

A:

Q: Find the second derivative of y = Vx² +x-3 O 6/x O 12/x^5 O 6/x^2 O 12/x^3

A: dxndx =n.xn-1 dcdx =0 ; where, 'c' is an constant number.

Q: Use the binomial series to find the Maclaurin series for the function. 4 f(x) = V1 + x %3D 00 f(x) =...

A:

Q: Secos(sin-tw)dv dv S- e2cos(sin¬{w) – 4 dv S- 4+ ecos(sin-w)

A: To find the values of dv such that the antiderivatives(integrals) exists.

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 3 Pa(x) =

A:

Q: sin 4zdz 18. 16+ sin * 2-

A:

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

A:

Q: Find the equation of the tangent line to f at x = a. f (x) = 3 − 4x,             a = 2

A:

Q: of salt has been dissolved. Another brine solution is pumped into the tank at a rate 5 gal/min, and ...

A:

Q: Find the radius of convergence and the interval of convergence. 2k+1 k2 + 49 k=1 Radius of convergen...

A:

Q: Activity 3. Solve the limit if the following given functions. Match Column A with Column B. Every an...

A: I am attaching image so that you understand each and every step.

Q: sech*2tdt

A:

Q: By considering appropriate curves which approach (0,0) (or other- wise), show that there is no value...

A: Continuity

Q: An iron rod at a temperature of is placed in a room at a constant temperature of . If after minutes ...

A:

Q: Question 2: Create a polynomial f(x) with real number coefficients which has the following character...

A:

Q: 3. Find the number of paths from A to B, travelling along the lines, downward or to the right.] A B

A: Number of paths from A to B is choose 5 from 11 . That is using combination 11C5

Q: 0<0 < , 3 cos 0 = Find the exact value of a) sin 28, and b) cos 29.

A:

Q: The integration expression Jsin(3In(x)+ 4)cos(3In(x) + 4)dx must be transformed into using suitable ...

A:

Q: lim e5x — 2e-2х + е-3х + 2е-5х —5е-10х n→0∞ 2х-4

A: Topic:- limits

Q: 4-4e" Evaluate lim,→0 3x+x15 4 15 - 4 15 4 3 -

A:

Q: L(cos(at)sinh(at))

A:

Q: Gauss-Seudel only

A:

Q: e +e =e**

A:

Q: COST OF DRILLING A 100-ft oil well is to be drilled. The cost of drilling the first foot is $10.00, ...

A: Given query is to find the cost of drilling the well.

Q: 12 Find the arc length of y = In(1 – 2²) on 0 < x < 19 No decimal entries. Find the exact value. L =

A:

Q: f(x)=∛(x-1) and g(x)=x^3+1 please explain

A:

Q: 4. [csch(x)] = -csch(x) coth (x) dx

A: we know thatdifferentiation of cosh(x) is sinh(x) and vice- versa

Q: For all n and m, evaluate: " sin na cos ma da

A: We have to solve given integration

Q: 1) Assuming that the pattern of the first few terms continues, find a formula for the general term a...

A:

Q: x-1 11. lim x² + 3x + 4 X-1 D. 8 17

A:

Q: Differential Equations: Give an example of an interconnected system of two tanks so that: the syst...

A:

Q: 2. The Left Coast Bookstore chain has two stores, one in San Francisco and one in Los Angeles. It st...

A: (a)

Q: What is the maximum of the function y = -x° + 3x for x > -1? O-4 O2 04 O-2

A:

Q: 3n+1 ба) n"

A:

Q: Using the bisection method, what is the approximate root of the function f(x) = x2 - sinx in the int...

A: I am going to solve the given problem by using some simple calculus to get the required result of th...

Q: Solve the given differential equation by undetermined coefficients. y" – y = x²ex + 7 3 У (x) %3D ce...

A:

Q: For a particular commodity, the demand function is q 300 - 15р. a. Find e when p = 10. Preview b. Is...

A:

Q: 4. lim x5 x- Note* the sign is negative -1/2 5. lim va N. -- I. 2v2 6. lim 3x Vx Н. 243 3 x-27

A: