VAI a. b. Given y =(x-2)²(3-x). Find the C. d. stationary points, interval of increasing and decreasing. inflection point and interval of concavity.

Q: Given f(6)=3, f′(6)=11, g(6)=−1, and g′(6)=7, find the values of the following (a) (fg)′(6)= (b)…

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Q: thats a natural log of 9 to 0 and integral from 9 to e^x

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Q: Find the optimal Solution of following transportation system formulated below by 1. Simplex method…

A: Let's solve by using simplex method.

Q: Find the general solution of the given higher-order differential equation. y""+ 2y" 16y'- 32y = 0…

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Q: Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100 mg…

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Q: =valuate the double integral [2aydA, 2xy dA, where D is the triangular region with vertices (0,0),…

A: Given that a double integration and given  D is  triangular region with vertices (0,0) (1,2) and…

Q: Evaluate using integration by parts: fx sec-¹x dx

A: SOLUTION-

Q: 5. Find the 6th term of the recursive sequence defined by a₁ = 0, an+1=2a₁ +3.

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Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

A: To find the critical points of the following function. By using the Second Derivative Test to…

Q: Show that y=sec^2x and y=tan^2x have the same derivative. What can you say about y=sec^2x-cot^2x?

A: Given y=sec²x and y=tan²x Now derivative dy/dx=d/dx( sec²x) =d/dx(1+tan²x) dy/dx= 2tanx sec²x   Now…

Q: 2 y = (x ² + 1)² Find dy dx

A: To find derivative.

Q: Consider the function. f(x, y) = 4 -1/3-2/4/20 Find Vf(x, y). Vf(x, y) =

A: Given :fx,y=4-x5-y4

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

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Q: W Identify the locations of transition points on the interval [2, 4]. (Give your answer in the form…

A: The given function is fx=2sinx+x We have to find transition points in the interval 2π, 4π.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: 5.x²=3(y-c)

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy - + y = f(x),…

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Q: Find the function f if. Vf-(3a²y + y², a² + 2xy), Vf dr with and without the Fundamental Theorem of…

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Q: a drug is injected into the bloodstream of a patient through the right arm, the drug ntration in the…

A: Topic:- application of derivatives

Q: Evaluate the following integral and express in exact form: cos(x/2) sin(x/2) dx

A: SOLUTION-

Q: Find the directional derivative of the function at P in the direction of v. == P(1, 2), v = -j f(x,…

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Q: Solve the differential equation by variation of parameters. y" + y = csc(x)

A: Our Aim is to solve the differential equation given below using variation of parameters.y"+y= csc…

Q: Estimate the area under the graph f(x)=1/(x+3) Over the interval (-2,1) Using 8 approximating…

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Q: Find the angle 9 between the vectors in radians and in degrees. (Round your answer for part (a) to…

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Q: 8.6 EXERCISES In Problems 1-10, classify each singular point (real or complex) of the given equation…

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Q: Complete the missing ones: (those highlighted ones) Integrate: .2x [cotcscdx 3 3 2x [cots (2) csc²…

A: Explanation of the answer is as follows

Q: z = cos(x² + y²), nd Əz/əu and Əz/av. The variables are restricted to domains on which the functions…

A: Use chair rule.

Q: Find the work done by the force field F(x, y, z) = 4xi + 4yj + 6k on a particle that moves along the…

A: Explanation of the answer is as follows

Q: 16. x²y" (x) + 5xy' (x) + 4y(x) = 0 ; y (1) = 3, y' (1) = 7 17. x³y"(x) + 6x²y"(x) +29xy' (x) -…

A: The given differential equation is;  x2y''(x) +5xy'(x) +4y(x)=0, y(1)=3, y'(1)=7.

Q: We have verified that x² and x5 are linearly independent solutions of the following second-order,…

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Q: Let Compute θω -(2, -3) = 28 მs дw -(2, -3) = Ət w = 4xy-yz - 3xz, x = st, y = est, z = ²

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Q: Find the absolute extreme values of the function on the interval. F(x)= == 3 21 0.5≤x≤2 OA. absolute…

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Q: on the closed triangular region with vertices (0, 0), (9, 0) and (9, 11). List the minimum/maximum…

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Q: Use spherical coordinates to evaluate the triple integral [[[ 2² + 3² + 2²dV, where E is the ball:…

A: We will first change it into spherical coordinate and then solve it.

Q: Average Cost Graph The total daily cost (in dollars) of producing a mountain bikes is given by C(x)…

A: Here we have to use the concept of derivatives. Suppose if f(x) is function defined on [a,b] Then…

Q: Compute the gradient vector fields of the following functions: A. f(x, y) = 1x² +10y² Vf(x, y) =i+ j…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: The indicated function y1x is a solution of the given differential equation.By using the reduction…

Q: Find the absolute maximum and minimum values of the following function on the given region R.…

A: To find the absolute maximum and minimum.

Q: Find the limit: lim (1- cos x) sin x+0+

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Q: Let f be differentiable at x = a. a. Find the equation of the line tangent to the curve y=f(x) at…

A: Given problem:- Let f be differentiable at x = a a. Find the equation of the line tangent to the…

Q: (a) to x = 8. Find the area of the region enclosed by y = x² - 4x and y = 2x from x = -2

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

Q: Evaluate the limit lim_ (8x² + 4) (6x + 8 →7

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Q: For what value of the constant c is the function ƒ continuous on (-∞, ∞)? cx² + 2x if x 2.

A: We know :- Limit definition at x=a  ⇒limx→a-f(x) =limx→a+f(x)  if function continous at x=a then…

Q: 4. State the parent functions and the transformation of the functions using proper order -3x-6 and…

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Q: Evaluate the following integral: Sºa dx -00x²+1

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Q: Rewrite the expression as a sum, difference, or product of logarithms. log 4 10x O log2 10 + log2 x…

A: To rewrite the expression

Q: 1. Given the following expression: 27 81 3 9 + + 10 100 1000 10000 a) Using sigma notation, write…

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Q: Use CRAMER'S RULE to solve the system : 2x-y-z = 2 4x + y -z =-5 6x - 2y +2z=17

A: To solve the system using Cramer's rule.

Q: 1²e¹dV where E is bounded by the parabolic cy E

A: the answer is give in step2

Q: M8 K-0 3 900+3k

A: Given, ∑k=0∞3900+3k