If the area under the curve, f(x), on the interval [1, 4] equals 6, what is the average value of f(x)?

Q: X √ ( - ² + x^² + 2]) dx 5

A:

Q: 2 dn = 5 n n!

A:

Q: Find an equation of the plane passing through the three points given P = (4, 2, 9), Q = (6, 7, 18),…

A: We have given three points as P = (4,2,9) Q = (6,7,18) R = (11,8,12)

Q: c) f(x) = secx sin.x d) g(t)= cost t²

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

Q: Evaluate the sum 1 Σ² n! n=0 1 + (-1)^²+¹ + (-2)' (−1)n+1 n 2n+1

A:

Q: Use partial fractions to find the area of the given region. 7 16x² y = y 3

A: Now area of the region f(x) from a to b formula Area=int_a^b f(x) dx

Q: What is the area between the curves y= integrating with respect to x.). O ! (6) WIN = ² and y=-x² +…

A: y=x2 and y=-x2+2x

Q: Determine the area bounded by y^2+4y=x-3 and 2x-y-3=0. Using a Horizontal Element.

A: The area bounded by the curves x = f(y) and x = g(y)  between y= a and y= b is given by…

Q: Let A=(¹). 3¹). Find 3A³2A² + 5A - 12.

A: Given: A=1-123 We are required to find: 3A3-2A2+5A-I2

Q: Let f(x, y, z) = x³y³ + z³ and x = s4, y = st², and z = s¹t. (a) Calculate the primary derivatives…

A: fx,y,z=x3y3+z3  and x=s4,y=st2,z=s4t

Q: Determine whether the following sequence is convergent or divergent. If it is convergent, evaluate…

A:

Q: 1) BASIC DERIVATIVES: Differentiate and simplify the following functions a) f(x) = 5x³+3x² - 5x+2 b)…

A: We know that the derivative of x^n Is  nx^(n-1)

Q: The owner of a skating rink rents the rink for parties at $540 if 30 or fewer skaters attend. For…

A:

Q: 6. For f(x, y) = x²exy Find fx (2,1) {needs product rule}

A:

Q: Given that v = (0, -2) and w = (5, -8), what is w - v? A (5,6) B (5,-6) C (-5, -6) D (-5, 6)

A: Explanation of the answer is as follows

Q: What is the area between the curvey and the x-axis on the interval from [0, 2]? O 128T OO CAT 128 7…

A: The given curves are: y=x6   and   x-axis  on the interval  0, 2

Q: (b) Evaluate [x² sin(x³) dx using substitution technique.

A: Substituting t as

Q: Sx.cos5(x²)dx

A:

Q: Solve the problem. At the Jumping Jack cookie factory, quality assurance inspectors remove broken or…

A: Equation of line passing through two points ( x1 , y1 ) & ( x2 , y2 ) is given as  y - y1 = y2 -…

Q: PROVE OR DISPROVE THE FOLLOWINCT: (SHOW FULL SOLUTION) 44 dx4 ((x ²³²= 1) inx) = 6 (x³71) x4

A: We have to proof that given expression. We know that  d/dx{f(x)×g(x)}=f(x)g'(x)+g(x)f'(x)

Q: Find the maximum value of the function f(x,y)=2x^2+3y^2-4x-5 on the domain x^2+y^2=121. List the…

A: To find the maximum value of the function fx, y=2x2+3y2-4x-5  on the domain x2+y2=121. To list the…

Q: Given the polar equation r = The eccentricity is e = 5 The equation of the directrix is: 7 6 sin(0)'…

A:

Q: What is the approximate volume of the solid created when the region under the curve y = cos z on the…

A:

Q: X-25 (x-2) √√x²+2x Converges? Dieverges? dx AND WHY?

A:

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A:

Q: Does the series converge or diverge? Please justify your answer in detail, mention any tests you…

A:

Q: Use the graph to estimate the limit of the function shown in blue as x→-1. O The limit does not…

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: (b) Use the function to find T(30,000). $ (c) Find the tax due on a taxable income of $120,000.

A:

Q: Use a table to find the Taylor polynomial P3 (x) for f(x) = √I-T around c = 2.

A:

Q: Find the area of the surface generated by revolving the curves about the x = sin t, y = 1 + cos t, 0…

A:

Q: Let M be a hermitian matrix. Fill in its missing entri- M = -3 -9 - 5i 1 - 2i -4 −6+2i 0

A:

Q: Connecting the Communication Device With the communication device pointed toward your home planet,…

A:

Q: The subject is: PrecalculusThe general subject is: Introduction to Calculusand the specific subject…

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

Q: Given below are descriptions of two lines. Line 1: Goes through (-4,10) and (0,4) Line 2: Goes…

A:

Q: 5 430 X 32°

A:

Q: Write the following numbers in Cartesian form (i.e., in the form a + bi). Use the principal value…

A:

Q: For an object whose velocity is given by v(t) = - +4, what is its displacement on the interval t = 0…

A: Given that valocity v(t) = - t2 +4. And interval is t=0 to t=3. We find displacement on this…

Q: log3 a³ b + 1 is equivalent to: O O 3log3(a)-log3(b + 1) O log3(a)-3log3(b + 1) O 3log3(a)-3log3(b)…

A: The expression is given by log3a3b+1 To write: The equivalent expression of the given expression.…

Q: True or False (Mean Value Theorem): For the function f(x) = 7+√ on the interval [0,9]. If f' (c) =…

A:

Q: 3. As light passes through water, it is gradually absorbed. The percent of light absorbed, 4, as a…

A:

Q: Find the general solution of the given differential equation. dy dx y(x) = (1+x) - xy = x + x² Give…

A:

Q: Find the general solution of the given differential equation. y dx - 3(x+y5) dy = 0 x(y) = Give the…

A: If the differential equation is of the form dydx+pxy=Qx then the solution of the differential…

Q: 4. Determine the vertex of the parabola y 2 2x + 15x using Calculus.

A:

Q: 2. S dx x√x4-4

A:

Q: Suppose f(x) = -4 6x + 6 can be written in the form Then the expression A (Ba+Ch+6)(Da + 6) "…

A:

Q: Find the Laplace tranform of the ff: e3xsin4x

A:

Q: If $17700 is invested at an interest rate of 6 percent per year, find the value of the investment at…

A:

Q: Consider the following vector function. r(t) = ( 26, 12², 1²) (a) Find the unit tangent and unit…

A:

Q: Determine all values of p for which the improper integral converges. [.. 7 dx Op> 1 Op≥ 1 Op<0…

A:

Q: What is the volume of the solid created when the region under the curve -4? (Solve using any y =…

A: