A company has the following production function for a certain product P(x, y) = 27 x0.3 y0.7 . Find the marginal productivity with fixed capital, Px .

Q: A: By using Linear equation solve the first order differential еquation y' + sec(x)y = cos(x)

A: The given differential equation is;  y'+sec(x)y=cos(x).

Q: Prove that f : [−4,2] → R defined by f(x) = 7/x+5 is uniformly continuous on the interval [−4, 2]…

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Q: * The solution of the differential equation below is dy = ky dx %3D x = eky y = ekx Option 2 O…

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Q: 1 18 6 The sum is (Type an integer or a simplified fraction.) 1/2 1/6

A: Topic:- sequence and series

Q: 10 sin x = 10 + 5 cos x %3D

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Q: Find the limit.

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Q: Consider the limits. lim f(x) = 6 x→7 lim g(x) = -8 Evaluate the limit using the limit law for a…

A: Evaluate the limit using the limit law for a quotient

Q: B: By using Homogenous method solve the first order differential equation (1+ e») dx - ely (G-1) dy…

A: Let's find.

Q: 5. S sin5x cos 3x dx

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Q: values of x in the open interval (0, 2) satisfy the conclusion of the Mean Value Theorem for the…

A: This question is related to Mean value theorem, we will solve it using given information.

Q: Find two linearly independent vectors perpendicular to the vector 4 -7

A: This question can be solved using the concept of linearly independent vectors.

Q: 1. The line segment from (1, –1,3) to (0, –3,1) forms a diameter of the sphere S1. Find the…

A: Given problem:- The line segment from (1,-1, 3) to (0, -3,1) forms a diameter of the sphere S₁. Find…

Q: Let 7. B(t) = ift < 2 - Vt+c ift 2 2. Find the value of c so that lim B(t) exists. t+2

A: This question is based on limits.

Q: Find the domain of the rational function. x-5 f (x) = x+8 Enter your answer in interval notation.

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Q: Use the Shell Method to compute the volume of the solid obtained by rotating the region in the first…

A: By using the Shell Method to compute the volume of the solid obtained by rotating the region in the…

Q: * This matrix is a 4 0 4 4 0 zero matrix square matrix diagional matrix O unit matrix O

A: This question can be solved using the concept of types of matrix.

Q: by the suitable solution Full the following blanks (Undetermined Coefficients method) If y" +y = 2x…

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Q: An Integration factor of this differential equation is .7 3x? + 1 + x3 dy 1 y : 1+ x2 dx

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Q: Consider the functionf(x, y) = 1x2 – 3y subject to the condition x² +y = 9. Use Lagrange multipliers…

A: We have to find the critical points and maximum, minimum.

Q: f(x) = lnx/sqrt(x) Find the first and second derivative

A: Given  f(x) = ln xx We have to find the first and second derivative.

Q: 5 (а). and the bottom of the box costs 3 TL per cm². The sides of the box costs 1.5 TL per cm². We…

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Q: Using appropriate substitution tan3. dx sec5x tan³x is equal to

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: By using Lagrange multipliers to find the maximum and minimum values of f subject to the given…

Q: Using Sandwich Theorem 3n2 + 1 an = (-1)" n3 – 4 | O diverges O converges to 1 O converges to -1…

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Q: Using Long (Euclidean) division then decomposition into partial fractions x4 – 4x2 – x - 3 dx x² –…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 18 - z…

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Q: Find the exponential function that contains the points (2,48) and (3,192).

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Q: prove that if the polynomial f(x) = x2n + a1x(2n-2)  +....+an-1x2 + an  is divisible by g1(x)= x-1…

A: prove that if the polynomial f(x) = x2n + a1x(2n-2)  +....+an-1x2 + an  is divisible by g1(x)= x-1…

Q: In this problem you will use variation of parameters to solve the nonhomogeneous equation t'y+…

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Q: 13. S /(1– cos x)dx

A: Follow the procedure given below.

Q: Find dy ldk 3x xナ+ チ= +メ

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Q: 9x2-42x+49 a. Simplify : 3x2-7x b. Solve the equations: i) 10 ii) 25x3 + 100x? – x – 4 = 0 ii) (х —…

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Q: This equation is an example for linear equations dy dx False O True O

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Q: Find the x- and y-intercepts for the function. x+1 r2+36 f (x) Enter your answers as points, (a, b).…

A: The given function is: fx or y=x+1x2+36   As we know that; To determine, x-intercept, we need to…

Q: Write an equation for a rational function with the given characteristics. Vertical asymptotes at x =…

A: Solution: Given data, Vertical asymptotes at x=-2 and x=4 So the denominator of the rational…

Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x 450. c and y = c – x² is…

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Q: Let y = (2x + 2 sin(x))“. Find f(x) and g(x) so that y = f(g(x)) and compute the derivative using…

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Q: Identify the graph of the curve by first sketching the graph of r as a function of 0 in Cartesian…

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Q: Find a formula for Sn, n > 1, if sn is given by 6 7 3' 5' 7' 9' 11 4 8 - Sn =

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Q: The surface area of a closed box is 200 square feet. If the width and height have the same…

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Q: Find the inverse of the function on the given domain. f(z) = (x – 14)2. [14, 0) f-1 (2) =

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Q: 3 xp- 4.

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Find the volume of the solid that results when the shaded region is 6 revolved about the indicated…

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Q: Let g(t) = 4t dæ a) Evaluate d 4t dx = dt b) Evaluate d dt c) Evaluate gʻ(t) =

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Q: Given the following functions: f(x) = cos(x) g(x) = x7 + 1 d d Find f(g(x)) and g(f(x)). (Use…

A: Given the following functions: fx=cosxgx=x17+1To find ddxfgx and ddxgfx.

Q: I z x sin(y²)d.xdy Calculate

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Q: By the Fundamental Theorem of Calculus: •t „2 +1 dx 5x +1 d dt d and dt - 6t x2 +1 dx 5x +1 d…

A: Given

Q: Find the domain of r(t) and the value of r (to). NOTE: Round your answer to two decimal places when…

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Q: sin Inx 12. S dx x cos² In x

A: Given integration is ∫sinlnxxcos2lnxdx We solve the integral using proper substitution.

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Given region is bounded by the function y=16x-2x2 and y=0 and rotating about y axis.