Let f(x) = { 8x6 if x < 10 - 4x + b if x > 10 If f(x) is a function which is continuous everywhere, then we must have b=

Q: Consider the following equation. =(21+√51) f(x, y) = y^/x, P(1, 3), u = (a) Find the gradient of f.…

A: Given :fx,y=y4x

Q: Let f(x)= = m= mx - 12 if x Next Question

A:

Q: Which term in the expansion of 2x is a constant?

A: 12x3-x58

Q: Determine the particular solution. (xy)dy – (3x² + y²)dx = 0; Y(1) = 1 O 3ln(x) + 12 = 1²² 2x² O…

A: Let's solve differential equation.

Q: (a) Find the domain of the following function, giving you answer in interval notation. f(x) = ln(x²…

A:

Q: Differentiate from the first principle f(x) = x² +6x² + 3

A:

Q: Use spherical coordinates to evaluate 2πT fff c2-r r+z (r² + z²) ³/ rdz dr de.

A: Given ∫02π∫12∫02-rr+zr2+z232rdzdrdθ

Q: 2. A person invests $2,125 in an account earning 9% per year compounded continuously. How much will…

A:

Q: 2. Given a tetrahedron with vertices (0,0,0), (3, 0, 0), (0,6 0), and (0, 0, 4). Express the volume…

A:

Q: Megan leased a car for 5 years at a rate of 4.80% compounded monthly. It required her to make…

A: Total amount paid after 5 years or 60 months = 665 x 60 = $ 39900 Remaining amount that she can pay…

Q: Show that any function of the form z = f(x + at) + g(x − at) is a solution of the wave equation a²z…

A: Given z=f(x+at)+g(x−at)To prove ∂2z∂t2=a2∂2z∂x2

Q: Let r(t) = 21²i+tj+t²k. (a) Find the unit tangent vector T(t) and T(3). (b) Find the principal unit…

A: As per our guidelines we are supposed to answer only first 3 sub-parts. kindly repost others.…

Q: II. L' Hôpital's Rule. Evaluate the following limits using L' Hôpital's Rule. 3-x 1. lim 1-3 2-8

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (a) Use differentiation to find a power series representation for f(x) f(x) 00 f(x) = n = 0 What is…

A:

Q: Find the distance of the point (2, 6, 4)  from the x-axis by two methods

A: To find the distance between the point.

Q: find the derivative using implicit differentation

A: Apply derivative on both sides

Q: If x > y and a are a negative real number, this always applies

A:

Q: Solve the following differential equation by using the Laplace transform techniques. d²x +8- dt² dx…

A:

Q: Air traffic controllers continuously monitor the angles of elevation and to an airplane from the…

A: Concept: The angle of elevation: The angle of elevation is the angle created between the line of…

Q: dy dx 2xy + 6x + (x²-4)-

A: Solution of given question is written in below steps.

Q: A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s…

A:

Q: 7. Let C be the portion of the circle x² + y² counterclockwise. (a) (b) Evaluate La xy dy. = 4 from…

A: Let's solve given integral.

Q: please explain how do we answer the question attached. Do we need to use a calculator?

A:

Q: Use power series operations to find the taylor series at x = 0

A: We have to find the Taylor series.

Q: Find the missing coordinate of the point, given that the point is in quadrant IV (₂ Oa). 5 √61 Ob)…

A:

Q: 7. The cost function for a particular product is given by C(x)=0.001x^3 −0.18x^2 +12x +200 dollars,…

A: Solution: C(x)=0.001x3 −0.18x2 +12x +200

Q: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given…

A: Given-

Q: Find the equation of the langents to the graph y-x3 3x2-15x-20 at the points of the graph where the…

A:

Q: ∞ Σ k=1 23k e-0.38k2 accurate to 10−5

A: We will find.

Q: The graph of f is given. Find the following or write d.n.e. if it doesn't exist. If a limit is…

A:

Q: Which of the following is the normal line at the point (-1, 1, 1) to the surface 2²-2y²-3²= -4…

A:

Q: Find the surface area of the torus generated by revolving the circle given by r = 5a about the line…

A:

Q: Find the interest rate needed for an investment of $9,000 to triple in 7 years if interest is…

A:

Q: L4Q12. Write an explicit formula for the sequence: - 2, 2, 6, 10, ... A.an = - 2 + 4n B.an = - 6 +…

A:

Q: The interest rate for a savings fund was 3.80% compounded semi-annualy for the first 4 years and…

A:

Q: f(x)=4 sin¹+x+√4x²

A:

Q: Shown to the right is a graph of f(x). (a) Describe the transformation for h(x) = -f(x + 1) +2. (b)…

A:

Q: Consider the following function: f (x) = -1/2 x^4 +16x^2 -4 Determine f′(x) and f′′(x).…

A: Solve the following

Q: Select all invertible transformations from the list below: Shearing Translation Scaling Projection…

A: Projections are not invertible transformation except we projects onto an entire space.

Q: Consider the function: f (x) = −6x/ 6x^2 − 54 Step 1. Determine the intervals on which the function…

A:

Q: Use the estimate |RN| ≤ b + 1 to find a value of N that guarantees that the sum of the first N terms…

A: Using the concept   RN≤bN+1 to find the value of N terms of the following series.          For  bn…

Q: The integrating factor of the given DE are already given below. What is the value of “n” ?…

A: We need to find n.

Q: Consider the following vector function. 12²) r(t) = (st, 1-², (a) Find the unit tangent and unit…

A:

Q: 6. Sketch an even continuous function with all of the following features: ✔✔✔✔ • Absolute maximum at…

A: We have to draw graph with given information.  Even function means symmetric about y axis.  Y…

Q: When demonstrating that lim suffices? 1 x-1 4x + 4 08= 0.0000025062656641604 OS=0.0000025 08=…

A:

Q: Determine the following indefinite integral. S dx x√√81-x 18

A:

Q: Find the general solution of the differential equation y"-y-6y 16e²t. NOTE: Use c₁ and ca for the…

A: Given  y"-y'-6y=16e2t

Q: What is the area of the region between the curves 3 y = x³ and y = x², from x = -3 to x = -1? Select…

A:

Q: Find an equation or inequality that describes the following object. A sphere with center (4,1,1) and…

A:

Q: 1) For each of the following tests, give an example and explanation of a specific series formula…

A: We have to explain the series and give an example.