How many 3-letter words can be made from the letters WASTEFUL if repetition of letters is allowed? repetition of letters is not allowed?

Q: eft co Evaluate cos² (9x) dx.

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Q: m #2: If ƒ(x) − x³ [f(x)]=-2x-12 and f(1) = 2, find ƒ'(1). - oblem #2: Enter your answer symbolica…

A: Given:- fx-x3fx4=-2x-12

Q: unction. (Enter your erivative. (Enter you

A: We have to find the following conditions according to the given information

Q: A) Consider the vector field F(x, y, z) = (6yz, 8xz, xy). Find the divergence and curl of F. div(F)…

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Q: Your job is to find some shortcuts for taking derivatives. For example, if the function is of the…

A: The derivative of a function at a point is the slope of the tangent drawn to that curve at that…

Q: Question #9 State Trapezoidal rule and use it to approximate the definite integral for the stated…

A: Trapezoidal rule: ∫abf(x)dx= h/2 [f(a)+f(a+h)+...f(a+nh)] h=(b-a)/n , n is the number of…

Q: Find dy dx dx y=6( cscX+ cotx)( cscX- cơ -0

A: Topic:- calculus and derivatives

Q: Consider the integral x3 2 √x + 1 Using the substitution u = √x + 1 the integral can be rewritten to…

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Q: Determine whether Rolle's Theorem can be applied to the function f(x) = (x+3)(x + 2)² on the closed…

A: Given that the function is         f(x) = (x+3)(x+2)2

Q: 11. f(x) = 2. h(x) 3. C(x) = = = 4. f(x) = 6. h(x) 7 f(x) = = 1 x+1 = -1 x+2 5 f(t)= t 5+2x 3+x x²…

A: As per our guidelines we can answer only three parts.please repost others seperately First of all we…

Q: Consider the following. f(x) = x(x² - 8x + 20) g(x) x² Exercise (a) Use a graphing utility to graph…

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Q: f(x) = 2x² + 3x + 1; 4² / + 24/1 = 8x+10

A: Topic- differential equations We are given f(x)=2x2+3x+1,we need to check whether f(x) is the…

Q: 16i + 12j. Find c π so that the angle between a and b is Let a = ci + j and b Round your answers to…

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Q: Find all relative extrema of the function. (If an answer does not exist, enter DNE.) f(x) = 2x² + 3x…

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Q: Find the following using the table below. 1 2 3 4 24 1 3 413 2 g(x) 3 4 2 1 g'(x) 1 4 2 3 x f(x)…

A: Find h'(1)

Q: differentiate (square root of x)/(1+x)

A: To find out the derivative of the function.

Q: 8) Use a graphing calculator to predict what income the company should expect in its seventh year of…

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Q: Determine the interval(s) over which the graph of f(x) = -x6-6x5+12x-2 is concave up or concave…

A: Given , f(x)= -x6-6x5+12x-2

Q: A 13-foot long ladder is leaning against a house when the base begins to slip away from the house at…

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Q: 1 ¹/ de by first rewriting the denominator as a single trigonometric function. cos + sin 0 3. Find

A: We need to find out the integration.

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

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Q: Express u = (6, -2) as a linear combination of v = (1, 1) and w (1, 1) and w = (1, −1).

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Q: A farmer plans to fence a rectangular grazing area adjacent to an existing fence. The grazing area…

A: The area of the grazing is 180,000 square yards. x.y = 180000           ....i) Required Fence = R.F.…

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

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Q: Use a graphing calculator to predict about how many books will have been read in the eighth grade…

A: Topic -estimation Grade number of books read 2 7 3 26 4 62 5 121

Q: Find the equation of the curve, if at any point on the curve y'' = 4x - sin 2x and that (π/2, 0) is…

A: Topic:- algebra and application of integration

Q: Homogeneous Equations Obtain the family of solution of the equation (x2 + 2xy - 4y2)dx - (x2 - 8xy…

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Q: Find the directional derivative of f(x, y) = direction of Q(2, −2). NOTE: Enter the exact answer.…

A: Solution

Q: Find an equation of the tangent line to the graph of f at the given point. 2 1x) = x + ² (1-³) f(x)…

A: The objective is to find the equation of tangent line.

Q: Find all critical numbers of the function ƒ(x) = sin²6x + cos6x¸ 0 < x < / Select one: a. b. C. O d.…

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Q: Find the curvature of the curve r(t) = (4t, – 5t³, 4t²) at the point t = 2. Give your answer to 2…

A: Vector calculation is required.

Q: Solve the differential equation below, when x = ; y = -4. 2 dy dx 5e cosx. If y(37) = a; find the…

A: I have appended the formula used in the solution part of the question

Q: Question 4. Evaluate the following integrals. (a) cos³ (tan x) sec² x dx (b) S 1 √4x²+4x+10 dx

A: ∫ cos3tanxsec2xdx

Q: Ali will rent a car for the weekend. He can choose one of two plans. The first plan has an initial…

A: Plan first  initial fees = $39.98 and cost on additional per mile driven is= $0.20  Plan second…

Q: adym by implicit differentiation. х2 + y2 = 36 Find dy C

A: to find out the implicit differentiation for the given function.

Q: A particle moves along the x-axis so that at any time t > 0 its position is given by a (t) = (at)²,…

A: Given the position of a particle is  x(t)=12(a−t)2

Q: The time for a chemical reaction, T (in minutes), is a function of the amount of catalyst present, a…

A: Here we have to use the concept of derivatives.

Q: Given the vector-valued functions ū(t) = e5ti + e¯4tj + tk v(t) = − 3ti – 2t²j + 3k

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Q: This set represents O a line O a half-plane, including the boundary O a half-plane, excluding the…

A: Solved below.

Q: Find the slope of the tangent line to the graph of the function at the specified point: b) y = 9…

A: We need to find slope.

Q: Consider the region R: Bounded by y = sqrt(2x), y = 0, x = 2 and y = x^2, y = 4, and x = 0. Using…

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Q: Find the vector component of v = (4, -1, 7) along b = (2, 4, -4) and the vector component of v…

A: Given; v=&lt;4,-1,7&gt; and b=&lt;2,4,-4&gt;.

Q: OF G Onone of these UF Which of the points are relative minima? (Select all that apply.) OA Ов OC…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Let's find volume by using shell method.

Q: Use cylindrical shells to find the volume of the solid formed by rotating the region bounded by y =…

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Q: Consider the function f(x)=5√x+9x^3+6x f′(x)=

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Q: 203. 1를 2-xdx 2 x² + x xx

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

Q: Let f(x, y) = 3x² - 8x + 3y + 2y² + 4xy. List the critical point: The critical point is a Select an…

A: Given function:- fx,y=3x2-8x+3y+2y2+4xy

Q: Find the points of inflection and discuss the concavity of the function f(x) = sinx-cosx on the…

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Q: Find all the critical numbers of y=x²-2x²-3, then determine the local minimum and maximum points by…

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