dy Given the equation below, find dx - 30x³ + 8x45y + y" : - 21 dy dx Now, find the equation of the tangent line to the curve at (1, 1). Write your answer in mx + b format y = -10x + 19

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A: Follow the procedure given below.

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Q: Continuity of Functions on an Interval Determine if the given function is continuous on each of the ...

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Q: Function Type Differential Operator ... AxN + BxN-1 + .+C DN+1 AxNeax (D - a)N+1 cos(Bx) or sin(Bx) ...

A: We will find the differential operator by the given table. We will use second row to find the requir...

Q: Explain why the Intermediate Value Theorem is not necess arily guaranteed fo f (x) = = CSC for x E (...

A: Topic = Functions   The intermediate value theorem states that if f is a continuous function whose d...

Q: Write as a decimal. (Type a decimal.)

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Q: Find the value of k so that the value of (2y - 1) dy is 10.

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Q: Sx+1)(3x – 2) dx

A: Evaluate , ∫x+13x-2dx=?

Q: Find Homogeneous DE y'-ay=0

A: Given that: y'-ay=0

Q: questions

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Q: Live equation ar differential with constat coefficients dx -3x 3x = -9ゼー1 5. | dt? dt

A: We have to find the general solution of differential equation

Q: Consider f(x) = 1 – x for 0 1: an b) O an = c) O ao = 1/2, and for n > 1: a, = 4(1+ cos(nT/2))/n²n²...

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Q: Find the domain and range of the function. Use interval notation to write your result. f(x) = sqaur...

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Q: 5. A wooden block is made as shown in the diagram. The ends are right-angled triangles having sides ...

A: Given Total surface area = 7.200 cm2

Q: x +1

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

A: Given problem:- Use the method of cylindrical shells to find the volume generated by rotating the re...

Q: graph of y = f(x) is shown. Use the graph to answer the question. Is f continuous at x = -4? 4+ 3+ た...

A: A function is continuous if left hand side limit and right hand side limit of function at a point ar...

Q: Performance Task *Limits of Transcendental Functions Complete the table of values to evaluate lim t-...

A: Since you have asked multiple question As per our policy, we will solve the first question for you. ...

Q: A tree on a hillside casts a shadow c = 230 ft down the hill. If the angle of inclination of the hil...

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Q: dx 1 3. xVx6 – 1 3 sec-(x³ ) + C

A: Let I=∫1xx6-1dxPut x6-1=u(squaring on both sidex6-1=u2x6=u2+1)differentiate 12x6-1ddx(x6-1)=du12x6-1...

Q: road length (in kilometers), T is the total county land area (in hundred-acres (Ha)), U is the urban...

A: We will find the number of accidents. 

Q: Find the arclength of y = 2x – 5 on 0 < x < 4

A: Topic:-  derivatives

Q: 2. (D2 + 3D)y = -18x: v = 0. Dy = 5 when x = 0

A: Given differential equation is  D2+3Dy=-18x  and the given conditions are y=0, Dy=5 when x=0 find th...

Q: Use the graph to find the limit (if it exists). Sx + 3, x + -1.5 lim f(x), where f(x) = { -3 ,x = -1...

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Q: 5. у %3D sin?(3x? — 1) 6. Р() %3D 4csc(sin3t) ans. y' = 6xsin(6x² – 2) ans. P'(t) = -12(cos3t)csc(si...

A: Topic = Derivative

Q: (x)

A: We will find the correct answer. 

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for th...

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

A: Topic = Volume

Q: Find the volume of the solid formed by rotating the region enclosed by y = e + 3, y = 0, x = 0, z = ...

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Q: Find the volume of the solid generated by rotating the region bounded by y = sin°(x) and y = 0 betwe...

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Q: Q2 (10 M)/ Are the following functions analytic? (a)f(z) = sin(z) (b) f(z) = Re(z) –i Im(z) %3D %3D

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Q: Find the value of k so that the value of "(2y - 1) dy is 10. 1 3 4

A: Topic = integration Value of k is 4.

Q: A tree on a hillside casts a shadow c = 225 ft down the hill. If the angle of inclination of the hil...

A: Topic = Trigonometry Height of the tree is 130 ft.

Q: How is the angle of a right-triangle changing as the adjacent side is changing? de Assume that the s...

A: Given, Adjacent=x Opposite= 20 Angel= θ

Q: Perform the indicated operation. If possible, reduce the answer to its lowest terms. 2 15 4 2 15 (Si...

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Q: Use the washer method to determine the volume of the solid formed when the region bounded by y = 3VT...

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Q: Given the first-order differential equation as below: (x² +3y² +5)dx +(6xy + 6y + 3)dy = 0 (i) Ident...

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Q: The half-life of cesium-137 is approximately 30 years. If an artifact initially contains 100 g of ce...

A:  decay constant k=ln2half life

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Q: Consider the following rational function: 1 anx" + an – 1x" + ajx + a0 ... f(x) bmxm + bm – 1xm + .....

A: Recall: Horizontal asymptotes of a rational function : Consider the rational function               ...

Q: Given a function f (x) whose graph is shown below. (6,5), (1,4) (-4,2), 2 (6,2) -6 -4 -2 2 4 -2마 9(1...

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Q: Complete the table to 5 decimal places and use the result to estimate the given limit to 4 decimal p...

A: topic - limits

Q: Calculate the first-order differential equation below using transformation y = xv. dy x+3y = 2x– y d...

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Q: Sx V1 – x² dx 3.

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Q: ghing 16 pounds stretches a spring feet. The mass is initially released from rest from a point 2 fee...

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Q: A central angle ? in a circle of radius 6 m is subtended by an arc of length 7 m. Find the measure o...

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Q: By how much cloth price rose during the

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Q: 4. A certain computer algorithm used to solve very complicated differential equations uses an iterat...

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Q: Sketch the region enclosed by a + y = 6 and æ + y= 0. Decide whether to integrate with respect to a ...

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Q: State the property presented 10 + (4 + 11) = 10 + (11 + 4) a. commutative property b. associative...

A: Here is given that  10+(4+11)=10+(11+4)