Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = -5 and g'(6) = 3. (Enter your answer as an equation in terms of y and x.)

Q: 1. Find the second derivative of the function. 8(x) = 3\/x + e7*In(x)

A:

Q: Select all that apply. Solve the following equation; domain 0° sx< 360°; sin?x - 7 sin x = 0 O 90 18...

A:

Q: Identify the system as independent, inconsist analytical method 1. x+y=4 *ーy=6 2. x+y=8 2x + 2y = 16...

A: Since you have posted multiple questions i can do first three question as per our company guidelines...

Q: Evaluate the double integral y sin(2³)dA where R is the triangular region with the three vertices (0...

A:

Q: Consider the following function. f(x) = %3D Find its average rate of change over the interval [9, 16...

A: We have to find ∆y∆x , f'(9) and f'(16)  Given f(x)=1x

Q: Use Simpson's Rule and n = 4 to find an approximation for the definite integral Vr +1 dr.

A:

Q: 00 1 1 dx x2 + x

A:

Q: Evaluate the improper integral if it converges, or else show that it diverges. 16 dx

A: Given query is to find the value of integral.

Q: Evaluate and graph the following: 1. lim(4 x) X-2 (x²-2x-3 lim 2. 海() x-3 x-3

A:

Q: 3. Evaluate: e-x²+2x dx (Hint: let t = (x – 1)²) %3D

A:

Q: 2x Use substitution to evaluate the integral dx (x² + 3)°

A: We have to apply rules of integration to solve the problem Power rule: xn =( 1/n+1)(x)n-1

Q: A point (3, - 1) on the terminal side of an angle 0 is given. Find the exact value of csc 0. 2/10 O-...

A:

Q: MULTIPLE CHOICE) Which of the following statement (s) is(are) true? I. y = e-/2 is a particular solu...

A:  Given perticular solution y=e^(-x/2)  And y=e^(2x)cos3x

Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (E...

A:

Q: 2. Verify that the infinite series converges 00 п a) E (:)" 6 n=0 00 n b) Σ-0. 6" n=0

A:

Q: In the decomposition a = aTT + aNN, what do aT and aN represent?

A: Tangential and normal component of Acceleration : Suppose that r→(t) is a smooth parametrization of ...

Q: 3. Evaluate: e-x²+2x dx (Hint: let t = (x – 1)²) %3|

A:

Q: Find the minimum and maximum of f(x, y, z) = y + 5z subject to two constraints, 2x + z = 4 and x² + ...

A:

Q: Solve the differential equation.

A:

Q: 3. Find the vertex form of the parabola tnat passes through the point (-1,2) and has a vertex (0,1/2...

A:

Q: cos 2x + 2 sin 2 x = _______

A: This question can be solved by applying the formula of cos2x cos2x=cos2x-sin2x

Q: DETAILS LARAPCALC10 2.2.014. Find the derivative of the function. g(x) = 4x² + 8x³ %3D

A: Given query is to find the derivative of the expression.

Q: The distance from the center of a hyperbola to its vertex is larger than the distance from its cente...

A: Given query is to find that statement is true or false.

Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

A:

Q: 2xyy'=1+y^2 solve using separation of variable (diff eq) when y=3 and x=2

A:

Q: A company that manufactures pet toys calculates that its costs and revenue can be modeled by the equ...

A:

Q: Coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 9 in./ min. Com...

A: Given:Coffee is draining from a conical filter into a cylinde rcoffee pot at the rateof 9 in3/min.To...

Q: Prove the following identities. sin 3x v 3 sin x - 4 sin cSC X - 2 sin 3 sec x - 4 sin

A: Given query is to prove the identity.

Q: A point (5, - 1) on the terminal side of an angle 0 is given. Find the exact value of sec 0. 2/6 3/2...

A:

Q: For the next six questions, consider the differential equation: y" + 4y = g(x), g(x)# 0

A: follow next step

Q: Evaluate the limit lim, 5 a. 2 b. 0 C -1 x d. I

A: Given: limx→5 x+11x-1

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given point...

A:

Q: Determine the intervals of continuity for the following function. AY 5- 4- 3- 2- 14 0+ 1. 2 3 4 6. 5

A:

Q: If f(x)=10sin(x)+3cos(x) , find a function g so that g"(x)=f(x) given that g(0)=0 and g(2)=12 . g(x)...

A: Given query is to find g(x).

Q: Determine all the partial derivatives of f(x,y, z) = y² In(x + 2y) – In(3z) (x³ + y? – 4z) Determine...

A:

Q: (MULTIPLE CHOICE) Which of the following equations is(are) exact? (A) (x - y3 +y sin z)dr (3ry? + 2y...

A: Given problem:-

Q: Iz + 기 b. lim x+ 8 ² +7x - 8) I-8-

A:

Q: 2-4 (2+4) Ba+C True or false? can be put in the form Explain. 2+4

A:

Q: -1 | tan *xdx

A: The given integral,       ∫tan-1x dx

Q: solve the differential equation: y(2xy+1)dx+x(1+2xy-x3y3)dy=o

A: Given diffrancial equation y2xy+1dx+x1+2xy-x3y3dy=0Solution :y2xy+1dx+x1+2xy-x3y3dy=02xy2dx+ydx+xdy+...

Q: A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 8 ft above the bo...

A: Note: Since you have asked part b, we will solve only part b. 

Q: f(2) Suppose that the limit value of: lim a , what does imply? g() O a. A limit exist. O b. The nume...

A:

Q: Problem 6 Consider a market that sells individual marbles. Qs=2+2*P Qd=11-P   A $3 tax on consumers ...

A:

Q: Let F(x) = f(x) + g(x), where the graphs of f and g are shown in the figure to the right. Find F'(3)...

A:

Q: Find the amplitude of the graph of gy=-7cos O 18% 7. 77 O-7 07

A:

Q: Use the Intermediate Value Theorem to show that the polynomial f(x) =x° +x - 2x + 12 has a real zero...

A: The objective is to find the correct option.

Q: Evaluate f x³e2x dx using integration by parts

A:

Q: sec®(x) dx S V cot(x V cot(x)

A:

Q: Given the graph of f(x) below, what is the value of c such that lim, se (z) - f(c)? O b. 1 OC -5 Od ...

A: We have to find where Left Hand Limit= Right Hand Limit= function value 

Q: Find (f^-1)'(a).  f(x)=4x^3+3x^2+8x+9,    a=9 (f^-1)'(a)=

A: Topic:- function and derivatives