Express 3p 12pq+4q² -1- 8p² 6p² +2pq as a single fraction in its simplest form.

Q: ƒ(s) = 4s - 18 9-s² What function f(t) has Laplace transform: 5s (s - 2)² +

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Q: Find dy/dx if y=2 – x^2.

A: Given query is to find the derivative of the expression.

Q: Question 1. A critical point of the function g(x, y) = ex y + 3x²y-y is (0,0). Use the Second…

A: Explained below

Q: Use the formula for the area of a trapezoid to evaluate √₂² (2x- 2 (2x + 3) dx.

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Q: Find the average value of the function f(x) = over the interval [0, 6] and find c such that f (c)…

A: We have to solve average value

Q: Let P be the set of points that belong to the shaded region imaginary The set P is (A) open (B)…

A: We can see that the outer boundary is not included in the region. So set is not closed.  We can see…

Q: 4. For the series Σ=1+()", does it converge and if so what does it converge to? * n²

A: We have to check that series 1/2*(2/5)n  where n=1 to infinity. Is convergent or divergent.

Q: The following differential equation (+1)² + ² = sin a dy dx x has an order of 0 0 O 3 O 1 02

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Q: Let f(x, y) = ln(x + y − 1). The domain of f is {(x, y)| x + y > }.

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Q: 77. an = (In 3 In 2) + (ln 4 − ln 3) + (ln 5 − ln 4) + - - + (In (n − 1) - ln (n − 2)) + (lnn − ln(n…

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Q: Evaluate f 10x(x² the following antiderivatives + 5) 7dx

A: The given integral is;  10x(x2+5)7.

Q: r = 7e0.70 ¬ the interval 0 ≤ 0 ≤ 1 and the straight line egment between its ends. -ea =

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Q: Given that F(x) = a) F'(x) bl 5'(4) 2 1 1 + 2 dt.Using the 2nd Fundamental Theorem of Calculus, find

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Q: a. Use limits to find the derivative function f′ for the function f. b. Evaluate f′(a) for the given…

A: The given function,    fs=5s3+3s, a=-3

Q: II. Trigonometric Substitution. Evaluate the following integrals using trigonometric substitution.…

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Q: Find f if f"(t) = 2e¹ + 3 sin(t), f(0) = −4, ƒ(ñ) = 9. f(t) = 2e^t-3sint-6

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Q: Two matrices A and B are multiplied to get AB if O both are rectangular both have same order number…

A: If A and B are two matrix then matrix AB is defined only when  (A) A and B are of same order (B) The…

Q: S(x + ex+1) dx 0 2. Sx5¹2 (x³ + x² - 7) dx 0 2x + 1 3. dx 2 0 e

A: Topic = Integration

Q: Find the unit tangent vector T(7) for the line tangent to the space curve r(t) = (12 cost, 12 sint,…

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Q: a. Find a curve with a positive derivative through the point (1, 1) whose length integral (Equation…

A: To find curve satisfying the given conditions.

Q: The first thing “e” wanted to do is to “Calculuize” his favourite game, apples to apples. So, one…

A: A box for the apples to apples game such that its width is exactly three times its length and its…

Q: Use the properties of the definite integral to express the definite integral of ƒ (x) = 6x³ − 4x² +…

A: Given :f(x)=6x3-4x2+2x-3interval [ 1, 3 ]

Q: 13. Find the distance from the point (2, 2, 3) to the plane 2x+y + 2z = 4.

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Q: II. Trigonometric Substitution. Evaluate the following integrals using trigonometric substitution.…

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Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(1, 1) =

A: The given function is;  f(x,y)=ln(x+y-1).

Q: Using the Inverse Function Theorem, what is (1-1) (8) given that /(x)=√√61-2? Note that (11) = 8.…

A: find inverse function

Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = 4 + xy - x - 2y, D is the…

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Q: consider the function f, such that f(x) = (ax + 3) * e*. If the slope of the tangent line to the…

A: Topic = Derivative

Q: Find the area of the region bounded by y = 6-x-x² and the x-axis 125 6 (a) A = square units 6 (b) A=…

A: The given curves are; y=6-x-x2 and x-axis or y=0.   Now find the x-intercept of the the curve…

Q: Use the quotient rule to evaluate h'(a) for the given function h(x) and a. 7x 9 - 2x Provide your…

A: A detailed solution is given below.

Q: Determine the domain of the function. 4x-7 4x + 36 f(x) = The domain is (Type your answer in…

A: Find out the domain of the function.

Q: Solve the initial-value problem. x(t) = x" + 3x' + 2x = 1 + t², x(0) = 0, x'(0) = 2

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Q: The figure shows a region in the complex plane. Write an algebraic description of the shaded region.…

A: Given :Center : Z0=4+i

Q: 11. Draw a high-quality graph by hand on graph paper for the function f(x) = 2x³ + 6x². Your work…

A: Given :  f ( x ) = 2x 3 + 6x2  find minimums , maximums and inflection points ,  And intercepts

Q: find the explicit solution of y' +xy = x√ y

A: This is a basic differential equation problem

Q: If 40 articles cost $35.20, how much does 1 article cost? What is the cost of 55 articles

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

Q: Which equation could be represented by the number line? A. -9+8 = -1 B. -4+ (-5) = -9 C. -1 + (-9) =…

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Q: A region bounded by f(x) 6 5 4 3 Find the volume of the solid formed by revolving the region about…

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Q: Assume that the random variable X is normally distributed, with mean μ = 70 and standard deviation…

A: To find the probablity P(X>a)  then we have to convert the expression into  Z-score value of the…

Q: x² - xy (x,y) (0,0) √√√√y If it exists, find lim Answer: .Write DNE of the limit does not exist.

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Q: Consider the graph of y = f(x) shown below in blue. Find the open interval(s) where f'(x) is…

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Q: Suppose w = x³yz + xy +z+3 and x = 3 cost, y = 3 sint, z = 2t. Then dw dt t= . [Show solution.] =

A: Given :w=x3yz+xy+z+3x=3costy=3sintz=2t

Q: ³ sin y - 3) = √10 ² Let f(x, y) dt 1 + cos² (t) 16 Then f (2, π/6)=

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Q: Use the matrices below to perform matrix multiplication. If the operation is undefined, enter NA. BD…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) [0, 12] r 2 X…

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Q: Given the functions: f(x)=x²³-7x g(x) = √5x h(x) = 9x-2 Evaluate the function (hog)(x) for x = 5.…

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: off f(x) dx, where Evaluate [ f(x) f(x) dx = f(x) = 18x², -T≤x≤0 19 sin(x), 0≤x≤T.

A: We have to solve given Questions.

Q: +√³1 (2) dx = -3 and ³ S If it is known that [²₁ √f (a) da = 4, find the value of f(x) dx.

A: To find out the integral value.

Q: = A region bounded by f(x) 9 8 Find the volume of the solid formed by revolving the region about the…

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Q: on. 2 2 x arctan(x²) --x)³ etermine the first three non-zero terms in the Maclaurin series for einz…

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