Find the function f(x), such that f(x)= In(3x) J ƒ(1)=1.

Q: Determine the indefinite integral 4 √√x + 3 6x 1/0² - 1717 dx 4 X

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Q: Question 1: Find the Laplace transform of the given functions by using the table of Laplace…

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Q: 1 x + ex 2 g dx

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Q: 3 S(x) = 6x² + x – 7 Find the coordinates of the point of inflection on and prove that it is a point…

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Q: Given yz = ln(x+ z), find dz and dz fie

A: As we know that; The Power law; ddxxn=nxn-1 The Chain rule; fgx'=f'gx·g'x And c·f'=c·f' ; where c is…

Q: Find the curvature and the radius of curvature at the point t = 0. x = e cos(t), y = et sin(t), z =…

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Q: Given the three vectors å ,b and ở in 3D. The following question is t termine if operation involving…

A: We can solve this as follows:

Q: A triangle is inscribed in a parabola such that the first vertex (point A) is at the origin and the…

A: This question can be solved using the concept of maxima and minima.

Q: Find the center of 8x 2 + 6y 2 - 32x + 24y + 8 = 0. (2, 2) (-2, 2) (2, -2)

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Q: Find the center of x 2 + y 2 - 10x - 8y + 1 = 0. (5, 4) (-5, -4) (-10, -8)

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: lim * 0 sin5x'

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Q: Gasoline is pouring into a vertical cylindrical tank of radius 5 feet. When the depth of the…

A: Volume of cylinder(V)=πr2hSubstitute r=5V=π52hV=25πhDifferentiate w.r.t 't'

Q: QI// Find the Area bounded by: x = -y2 and x =y-2

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Q: -1

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Q: Q2// Solve the following differential equation: e2y dx + 2(xe2y – y)dy = 0

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Q: thu2 Evaluate khe faltowing cartesian integratby - changing them inte equivalent Polar integrals 2.…

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Q: At which point or line is the graph of r = 2 sin 0 + 2 cos 0 symmetric ? Select one: O the pole O…

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Q: Find dy/dx: 1. y = J" cos t dt

A: Given

Q: a²z Determine if z = tan- + r2+02° r

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Q: 19x + 900 The average cost for a company to produce x units of a product is given by the function…

A: To find change in average cost as production goes from 150 to 151 units.

Q: Use the formula к(t): k(t) ||r' (t) x r"(t)|| 3 ||r' (t)||³ r(t) = esti + e¯tj = to find (t). #1

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Q: Let the graph below represent an object's velocity as moves away from a sensor. At what time, in…

A: This integration can also be found from area under the curve .

Q: Find the area of the region under the graph of the function f on the interval [1, 5]. f(x) = 3x³…

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Q: Let C be the parametric curve defined by x(t) = t² – t – 2, %3D |y(t) = t3 . 1 t² +t. 2 - (-2) 3…

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Q: Select all of the following tables which represent y as a function of x. y -2 -1 -2 -5 -1 2 1 2 1 1…

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Q: Find the x-value maximizing the shaded area on the interval 0 < x < 18. One vertex is on the graph…

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Q: 6 Select the conic section represented by the equation. 5x 2 + 5y 2 = 0 point hyperbola  line…

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Q: Find the exact length of the curve. y2 = 64(x + 1)3,   0 ≤ x ≤ 1,  y > 0

A: Given,             y2=64x+13 , 0≤x≤1 , y&gt;0To find : Find the exact length of the curve.

Q: Evaluate y' of the given functions y = /3x + 4)(x + 3)

A: We can find the derivative as below.

Q: Find each limit, if it exists. (a) lim + 4 x-00 x - 3 X4 + 4 (b) lim X 00 x -3 + 4 (c) lim X- 00 x3…

A: All the limits are in indeterminate form, just taking common  some power of x from numerator and…

Q: Current Attempt in Progress Describe the graph of the equation. 14 sin 9t i + 14 cos 9t j r = It is…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: is the graph a function?

A: To determine whether the given graph represents a function.

Q: Given the two vectors: å = 2ỉ -j+k, b = i + 2k and d = 3ỉ + 5j in 3D. a) Determine the dot product…

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Q: Find the focus of the parabola y = x 2 - 12x. (6, -35) (6.75, -36) (6, -35.75)

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Q: 5x-10 Find the area under the curve of f(x)=- 05 O-10In 2 O 5-10lm 2 0-5 from 1 to 2.

A: Solve the given

Q: From a building across the street, the angle of depression of the foot of an edifice is measured as…

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Q: Solve the given differential equation by undetermined coefficients. y'' − 12y' + 36y = 24x + 2…

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Q: If x-8 A B then the value of A is (x+1)(x-2) x+1 x-2 and the value of B is

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Q: Evaluate the definite integral. 18t (elst i+e¹j+t k)dt S (¹²¹ ₁+ (e-1) i-(¹-1) j+k els 1 - (e¯¹ − 1)…

A: Follow next step

Q: A rectangular solid (with a square base) has a surface area of 37.5 square centimeters. Find the…

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Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

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Q: . Write both an absolute-value and a piecewise function to represent the graph.

A: 5. Absolute function  take graph of f(x)=|x|shift graph 3 units to right and 2 units…

Q: ſ(2x+5)dx Use geometry to evaluate

A: Follow next step

Q: Consider the polar equation defined by r = 5 cos(2 sin 6), where 0<0< 27. Determine the missing…

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Q: Is partial fraction decomposition always possible? If YES, Explain If NO, Explain

A: We have to explain given statement.

Q: 22. Differentiate. y = asinh x

A: Given,  y=xsinh x

Q: Consider the polar curves Cı :r = 3 sin 20 and C2 : r = 3 cos 0, and let R be the shaded region as…

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Q: Show the repeating decimal .2727272727 repeating.... as an infinite geometric series. Give sum of…

A: This question can be solved using the concept of infinite geometric series.