The functions f and g are continuous and differentiable with g(x) = f'(x). Selected values of the functions f and g are shown in the table below. What is the average value of g(x on the interval [0, 6] in simplest form? 2 3 f 3 -2 -8 -7 -1

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

A:

Q: Find the derivative of the following using First Principle. 1) y = 1 2) у %3D х 3) f(x) = 5x3 %3D 4)…

A:

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A:

Q: x'sec'ydy – (1 – 2x²tany)dx = 0

A:

Q: 4. Consider the function f(x,y) = 4 + x³ + y² – 3x – 4y a. Find the values of x and y that…

A:

Q: x(1-x')y = x' + y-2xy? ソ=

A:

Q: Bernoulli's Equation Solve:

A:

Q: The graph shown below is fx) = x + 1. What is the integral function g(t) that defines the area under…

A:

Q: The graph shown below is f(x) = 2 cos x. If g(x) = Sřf(t)dt , find g '( 1 ). %3D 4 3- 2- 54 3 2 -1 1…

A: Use the Newton Leibniz Theorem and calculate the derivative.

Q: d) 2x³y + e2y = 4x + 5x²< e) y = (2x* + 4)4*

A:

Q: y^2=(x^2 - 9)/(x - 4) find the x and y intercept, symmetry, region/scope, asymptotes, critical…

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A: This question is based on 3d line equation.

Q: g (x) = sin(x) Compute IT IT + g' + g" 2

A: This question is based on derivative of a function.

Q: Answer the following True or False. If f(x)dx 0 and f(x) is continuous, then a = b. O True O False

A:

Q: Use the series representation for cos x, cos x = 1 – + to find the following three items: 6! 1- A…

A:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) = 4i +…

A:

Q: ................................................. Determine whether the lines intersect, and if so,…

A:

Q: CSC* x dx cot2 x cot²

A:

Q: ). Determine whether the Mean Value Theorem applies to f(x) 3r + (1,4). -). If so, find the point…

A:

Q: What would happen to the volume of the cone if the radius of its base is tripled and the height is…

A:

Q: Consider the following. u = 5i - j - k, v = -i + 5j + 2k (a) Find the projection of u onto v. (b)…

A: The expression for the vector projection of u onto v is: projvu=u·vv2v And The expression for the…

Q: Integral Calculus: Integration by Parts (Original method

A:

Q: Evaluate the integral below by interpreting y=(x) it in terms of areas in the figure, A1 A3 The…

A:

Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: (0, о, 16), (12, 12, 0) (a) parametric equations (Enter your answer as a comma-separated list of…

A:

Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

A:

Q: Direction: Solve the following equations using separation of variables. 3. 2xy + 6x(x² – 4)y' = 0…

A:

Q: Let there be the random vector Z E Rm Prove that E (||Z||*) = tr(E[ZZ"]) From the expression above,…

A: The answer is in step 2.

Q: /Factored) Evaluat the indefinite Integral. Write your answer in xp गके एके +उमणेप्याउ 1- et:

A: To evaluate: I=∫x+2-1dx

Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 3, 4) (b)…

A: Given: xyz=12 (1,3,4)

Q: 3. x'sec'ydy - (1– 2x'tany)dx = 0

A:

Q: 3- use Cramer's rule to solve the system 8x1-4x2+3x3=0 X1+5x2-X3=0 -2x1+6x2+X3=0

A: Here we have to use Cramer's rule to solve the system.  8x1-4x2+3x3=0x1+5x2-x3=0-2x1+6x2+x3=0

Q: A cubical container that measures 2 inches on a side is tightly packed with 8 marbles and is filled…

A:

Q: f(x, y) = e2Y sin(x), P(0, 0), Q(2, 1)

A: Use the formula for the directional derivative and simplify.

Q: 2z2 + 7z +4 Let f(z) = 1³ + 2x² + 2z [1] (a) Write the general form of the partial fraction…

A:

Q: Using the partition method, find the inverse of 4 3 1 - 1 3

A:

Q: Given the hyperbola with the equation y – 9x? = -9, find the vertices, the foci, and the equations…

A:

Q: a). Find the linear approximation to f(x) = VI at r = 64, (b). Use it to approximate V65. c).…

A:

Q: (i) re dr -2

A:

Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A:

Q: Consider the function: f(x)=4−6x^2, −4≤x≤1 . The absolute maximum value is: And this occurs at x=…

A:

Q: The Maclaurin series for f(x) = x²e=* is E-o(-1)" xn+2 п! False True

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

Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: g (x) .5 Compute g(1) + g' (1) + g" (1) + g" (1) + g'

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A:

Q: Direction: Find the differential equation of the family of curves described. 4. Ellipse with center…

A: Equation of ellipse is x^2/a^2 + y^2/b^2 = 1

Q: 5. The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the…

A:

Q: (x² + y² ) dx – xydy = 0 O 2y = x In cx² O y? = x² In cx²

A:

Q: 2. Find an equation of the sphere satisfying the given conditions. a. It is concentric with the…

A: In this question, we want to find an equation of a sphere which is concentric with the given sphere.

Q: 2. y = loga(x³ + 2x – 2) 3. y = In³ (x + sin x) %3D 4. y = tan¬1(3x)

A: