Find the derivative of using the chain rule: f(x)= csc x^3 answer the question correctly and explain it step by step. use the formula: d / dx csc u = -csc u cot u du

Q: Calculate the line integral f(−3xy³ – 10x − 3y – 5) dx + (−xy − 10) dy, - where C' is the rectangle…

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Q: Define a function f: R → R by the formula f(x) = 2x - 9. Prove that fis onto. eBook Let y E R. Then…

A: Given f( x ) = 2x - 9 let y ∈ R , then f ( y + 92 ) = ?

Q: If C is the curve given by r (t) = (1 + 3 sin t)i + (1 + 1 sin² t)j + (1 + 1 sin³ t)k ,0 ≤ t ≤and F…

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Q: f'(x) <0 for x# -5 Choose the correct graph below. A. Choose the correct graph below. A. -10 Choose…

A: Given query is to find the correct graph: Solving A and B since graph of C and D are not given .

Q: Find the work done by the vector field F = (4z, 4y, 3x) in moving an object along C in the positive…

A: Solve the following

Q: Find the derivative of f(x) = (x8 – 9x) (x² = + 2x -6)

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Q: Given the equation y The amplitude is: The period is: = The horizontal shift is: The midline is: y =…

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Q: Find the Taylor polynomials P₁. P₁(x)= P₂(x) = P3(x) = P4(x) = **** P4 centered at a=0 for f(x) =3…

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Q: Use the Shell Method to calculate the volume of rotation, V, about the x-axis for the region…

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Q: Use the properties of logarithms to write each expression in Problems 39-42 as a single logarithm.…

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Q: 2 1 1 √1–1² SS dzdxdy 0 y 0 Rewrite using the order dz dy dx

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Q: 11. If csc 0 = -and has its terminal side in Quadrant III, find the 3 exact value of tan 20.

A: use the trigonometric identity formula for finding the given angle

Q: Use the substitution X 2 sec t to evaluate the integral - = dx x√x²-4

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Q: Find values of a and b, for which the following vectors are parallel: (8, a + b, 6), v = (4, 3, 2a —…

A: Given:   u = ⟨ 8 , a+b , 6 ⟩     v = ⟨ 4 , 3 , 2a - b ⟩

Q: Answer the following questions about the function whose derivative is given below. a. What are the…

A: To get critical points of f(x) we put f'(x)=0

Q: Given the vector-valued function u(t)= (t²- 3)i + (2t + 4)j + (t³ - 3t)k, d calculate [u(t) × u'…

A: Explanation of the answer is as follows

Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

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Q: Use the guidelines of this section to sketch the curve. f(x)= x(x-4)3 -6 O -5 -4 f(x) 40 20 x -6 -4…

A: The given function fx=xx-43. We have sketch the graph of the function.

Q: (1) Let y = Σnz". (a) Compute y' and write out the first four terms of the series. (b) Compute y"…

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Q: The minute hand on a watch is 8 mm long and the hour hand is 4 mm long. How fast is the distance…

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Q: A carbon sample contains 4000 atoms of radioactive element 235U. Given that 235U has a half-life of…

A: A carbon sample contains 4000 atoms of radioactive element 235U. Given that 235U has a half‐life of…

Q: A circular arc has measure 13 ft and is intercepted by a central angle of 2pi/3 radians. Find the…

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Q: A. An angle between 0 degrees and 360 degrees that is coterminal with -30 degrees _____degrees

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Given the information below, estimate the total distance traveled during these 6 seconds using a…

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Q: At a bowling alley, the cost of shoe rental is $2.25 and the cost per game is $4.25. Iff (n)…

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Q: A population of a particular yeast cell develops with a constant relative growth rate of 0.4461 per…

A: The answer is given below:

Q: 0 4 √t dt

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Q: lim x→0 7x sin 4x

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Q: 7. -ydx + (x + √xy)dy = 0

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Q: Suppose that an object initially having a temperature of 20°C is placed in a large temperature…

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Q: Estimate the area under the graph of f(x) = x² + 2x + 1 over the interval [2, 6] using four…

A: To estimate the area under the graph of fx=x2+2x+1 over the interval 2, 6using four approximating…

Q: Evaluate, using substitution f 24t5 4t6 +3 - dt. T

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Q: Consider the following parametric equations. Answer parts a. through d.   x=t2​, y=t−3​; −4≤t≤4   a.…

A: Solve the following

Q: A cup of hot coffee whose temperature is 200°F is poured in a room whose temperature is 70°F. Two…

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Q: DC The graph below shows two linear functions, f(x) and g(x). For values of x shown on the graph,…

A: We know equation of line passing through points x1,y1 and x2,y2⇒y-y1=y2-y1x2-x1x-x1

Q: D 8 (2 sin x cos x) (csc (sin³x + 1))

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Q: Find a cosine function and a sine function whose graph matches the given curve.

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Q: Use linear approximation, i.e. the tangent line, to approximate √16.4 as follows: Let f(x)=√. Find…

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Q: 6 Find the circumference of the circle pictured above. Round your answer to the nearest tenth

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Q: Find the perimeter and area of the given figure, using the correct unit of measure

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Q: Find the distance in exact form between the point P(−4,1,0)(-4,1,0) and the point Q(−3,3,2)(-3,3,2).

A: concept Let two points   ( x1,y1,z1 )  and ( x2,y2,z2 ) then distance between them is denoted by = P…

Q: Does the geometric sequence converge or diverge? Explain. 40, -10, 2.5, -0.625,... The sequence…

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Q: Find a function of the form y = A sin(kx) + Cor y = A cos(kx) + C whose graph matches the function…

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Q: The growth of a certain bacteria population can be modeled by the function A(t) = 500e 500e0.0572t…

A: Given query is to find bacteria growth at different points.

Q: 8. 2 sin² x 5 sin x + 2 = 0

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Q: Suppose you are standing such that a 36-foot tree is directly between you and the sun. If you are…

A: Since two triangle are  symmetrical h36=180-160180h36=20180h36=19h=369h=4

Q: 19 60

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Q: f(3) f(9) f(x) dx 3 9 [² x f(² 9 x f(x) dx x² f(x) dx Evaluate: = = = 8 6 16 18 = 13 9 ( − 8x + 6)…

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Q: Use the substitution x = 7 sint to evaluate the integral ſ √49 – x² dx.

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Q: The demand for tickets to an amusement park is given by p= 80 -0.04q, where p is the price of a…

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