Suppose you know that f(8) = - 1, f'(8) = 10. Find the equation of the line tangent to the graph of 3 3 x + y + y³ − 360 = x² f(x) at x = 8. - The line passes through the point with slope The equation of the line will be

Q: Solve the given equation in the interval [0,2 π]. Note: The answer must be written as a multiple of…

A: This question can be solved using the concept of solution of trigonometric equations.

Q: If ả = 2ỉ + 33, b = j – ỉ and ở = 33 are vectors in 2D, then determine the of a + 3b + c

A:

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

A: Use root test to check the convergence of series.

Q: Find the limit. lim (t i − 3 j + t² k) 1-5 lim (t i − 3 j + t² k) − i 1-5 i k = i+ i j+

A: We can find the exact answer as below

Q: Calculate d^2 f where f(x,y)=e^x sin⁡y.

A:

Q: Write the equation of a sine or cosine function to describe the graph. 'y 4- 0 NA 3 9 15 4 2

A: we have to find sine function.

Q: 1. Evaluate 2 0 X √1+ 2x² -dx

A: Answer is in step 2.

Q: Find two positive numbers that satisfy the given requirements. The sum of the first number squared…

A: We have to calculate first and second number

Q: 2. Consider the following table of a periodic function h(t). t 0 1 2 3 4 5 h 4.0 5.25 6.165 6.5…

A: hmin =1.5hmax=6.5A)Midline:y= hmax+hmin2y=6.5+1.52y=4B)Amplitude:A=hmax-hmin2A=6.5-1.52A=2.5

Q: The parents of a child wish to establish a trust fund for the child’s college education. If they…

A: Compound Interest Formula:  (compounded continuously) A = P·er·t where t is the time period in years…

Q: 21 te 1 1 1-2 1-2 None of the alternatives are correct If L <=lim In p-400 then f(t) is 0+2

A:

Q: Write an equation of the form y=a sin bx or y=a cos bx to describe the graph below. y 0 4 5 16 7 8 9…

A: Given

Q: Select all of the following tables which represent y as a function of and are one-to-one. I 5 8 8 Y…

A: Given query is to find which function is one to one.

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A:

Q: Find the average value of the function F(x,y) = x³ex++ the region 05x≤2 and 0≤ y ≤ x². over

A: Given problem:- Find the average value of the function F(x, y) = x3 exy +(y/x)2 +(y/x)  the region 0…

Q: Use the ratio test to determine whether Σ n=10 converges or diverges. n(-3)n n!

A:

Q: The function f is defined as follows. 2x if -2<x<0 f(x) = x³ if x20 (a) Find the domain of the…

A:

Q: The area of a triangle with sides of lengths a and b 1 and contained angle is A = a b sin 0. If a=2…

A: Use the application of derivative to find the rate of change.

Q: The plane region is revolved completely about the​ y-axis to sweep out a solid of revolution.…

A: We want to find the volume of revolution on  about the y-axis

Q: 1. Use the graph of y = f(x) given below to find the answer to each of the following. You do not…

A: By using the graph of y=fx given below to lisy all the intervals on which f is increasing.

Q: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 7A…

A: Area of the Rectangle =(Length)(width). Perimeter of the Rectangle=2(length+width).

Q: Find the future value of a $30, 000 annual income stream if it is invested immediately as it is…

A: Solving the problem by finding the value of compound interest.

Q: x² +9+√√√y²+1=5 max x + y

A: Given problem:-

Q: дz State the multi-variable chain rule for du z=z(t, s), t=t(u, v, w), s=s(u, v, w) if

A:

Q: Find the arc length L of the graph of r(t). r(t) t L= = ³²³i + 1 j + 1/2 √√61² k, 25157 = i

A:

Q: Use the First Derivative Test to find the location of all local extrema for the function given…

A:

Q: h(x) = f(gx)) calculate the following derivatives using the table a) h'(3) b) h'(2)

A: Given

Q: Suppose that Po is invested in a savings account in which interest is compounded continuously at…

A:

Q: QUESTION 12 dz State the multi-variable chain rule for if ди z=z(t. s, w), t=t(u, v), s=s(u, v), w=w…

A:

Q: Q1: Find partial derivatives of the function with respect with each variable 3) f(x, y) = (xy-1)² 2…

A:

Q: Given the function f(x) = -1+52², calculate the following values: f(a) = f(a+h) f(a+h)-f(a) h =

A:

Q: This is the length of the major axis, not the minor axis.

A: Apologies for the inconvenience.   Given equation is: 7x2+y2=49 We write it in the form: x2a2+y2b2=1…

Q: Determine whether an exponential function, a logarithmic function, or a linear function is the best…

A: Given the query is to find the best fit function.

Q: 21. Find 1² [f(x) + 28(x)] dx if [²₁ f(x) dx = 5_ and ₁8(1) g(x) dx = -3

A:

Q: 1. Find the derivatives of the following function (a) y=4²+2√² (b) y=++ 2x+3

A:

Q: Evaluate the integral. JS 2x + y dA D where D is the region bounded by y=x, y=0, x=2.

A:

Q: Plot each of the given complex numbers in an Argand diagram and label all the necessary parts. Also,…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Write the conjugate of √a +3

A:

Q: 4. Use mathematical induction to prove the truth of each of the following assertions for all n ≥ 1.…

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Q: Question 6 The domain of the function f(x)=√-4x+12 consists of one or more of the following…

A:

Q: Use AMNP, as needed, to complete the given parts. 18 cm 15 cm h cm 16 cm Part 1: Part 2: Part 3:…

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

Q: Q1: Find partial derivatives of the function with respect with each variable 2) f(x, y) =…

A: As per guidelines we can answer only three subpart questions at a time, so if you need more answers…

Q: Given the function f(x) = 3x - 7, evaluate and simplify the expressions below. See special…

A: The function is given by fx = 3x-7 To evaluate: The values of fa, fa+h and fa+h-fah

Q: NOTE: When using interval notation in WeBWork, remember that: You use 'INF' for oo and '-INF' for…

A:

Q: y = 2-ex 3x-1

A: We know that differential power rule is given as - d(xn)/dx = nxn-1.   Here i attached the solution…

Q: Consider sin¹x cos³x dx. If we let u= sinx, the integrand can be transformed to

A:

Q: Find the average rate of change of f(x) = 5x²-9 on the interval [2, t]. Your answer will be an…

A: Use the formula for the average rate of change of a function.

Q: Find the laplace transform of ƒ (t) = 2t³ – 6t – 8 -8s³+12s-6 OF (s) = 84 OF (s) 6s³-8s-12 84 ○ F…

A: Given that,  f(t)=2t3-6t-8

Q: A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 600 yd…

A: A rectangular swimming area in front of Long Lake Beach, using 600 yd of rope and floats.

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r =…

A: