Differentiate the following function. You do not need to simplify the derivative. f(x) = (lnx)5 f'(x) =

Q: Consider the function f(t) = 10 sec² (t) - 3t³. Let F(t) be the antiderivative of f(t) with F(0)…

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Q: Find the derivative of the given function. g(x) = sec¹(2πx) a) g'(x) = 87 sec³ (2πx) tan(2x) Ob)…

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

Q: Solve the following (i) 33x-5- = 9/x equations: (ii) 22x+2 = 42x-1

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Q: Evaluate the definite integral. 6.³ sin(3t)dt

A: The given integral is Sin(3t), limit from 0 to pi/3.

Q: a. b. C. d. e. x² + 4x + 16 2 x² + 8x + 8 2 x² + 8x + 64 +2 x² + 4x + 5 2 x² + 8x + 16

A: Observe the mixed term and then guess the possibilities.

Q: When completing the square for the quadratic equation shown below, how is c calculated?

A: Our Aim is to show how c is calculated when completing the square for thequadratic equation…

Q: Evaluate: [² 3 x³dx -

A: Here we have to find the definite integral.

Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

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Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of y=-x² + 7x between x = 1…

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Q: For the following graph the equations and shade the area of the region between the curves. Determine…

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Q: What are the parametric equations of x - 2y + 3z - 1 = 0?

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Q: True/False: Answer a) for True, b) for false and mark on the scantron. 24. The following is a…

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Q: Solve the equation (x+3x³ siny) dx + (x4 cosy) dy = 0

A: Here we have given a differential equation :(x+3x2siny)dx+(x4cosy)dy=0      ......eq(1)

Q: ) In the following exercises, use direct substitution to show that each limit leads to the…

A: The objective of the question is determine the limits of the given function.

Q: Solve the following differential equations y" - y'= 4cos²x

A: We have to solve the differential equation y''-y' = 4 cos2x

Q: A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 7,…

A: To find out the position of the particle.

Q: Let C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line segment…

A: Answer is in next step, please give a like!!

Q: If evaluate f f(x) dx = 7 f(x) dx = 8 f2f (x) dr.

A: Topic = Integration

Q: Find equivalent polar coordinates (r', 0') satisfying r' ≥ 0,0 ≤ 0¹ < 2π for the · (-1, (c) point…

A: Solution is given below:

Q: 2- The circle ² + (y-2a)2 = 4a² is rotated about the line y = -1 where a > 0. A torus is obtained…

A: Given: the circle x2+(y-2a)2=4a2 is rotated about the line y= -1 then torus is obtained from this…

Q: [xt xtan xdx

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Q: Using the definitions of tanh and sech in terms of the exponential function, solve for x 4 sech(3x)…

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Q: Find the complete solution of the linear system, or show that it is inconsistent. (If the system has…

A: Given: x+3y-2z=02x     +4z=44x+6y     =4

Q: Find the area of the region enclosed by y = 6x² and y = x² + 1. Round your answer to three decima…

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Q: Given f''(x) = 7x + 4 and f'(0) -2 and f(0) - 3.

A: Given that f"(x)=7x+4 and f'(0)=-2 and f(0)=-3Our Aim is to find f'(x) and f(4)=?

Q: (a) Find the critical numbers of the function f(x) = x(x - 2)5. X= (smallest value) X= X= (largest…

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Q: A writer wrote 850 words on the first day, 730 words on the second day and 610 words on the third…

A: Given: A writer wrote 850 words on first day, i.e. d1=850 Similarly for second and third day…

Q: Determine the common ratio r, the fifth term, and the nth term of the geometric sequence. 4 8 16…

A: We know that the nth term of a geometric sequence is given by  a·rn-1 where a is the first term and…

Q: Consider the plane π : x − 2y + 3z − 1 = 0 and the line l : x = (1 − y)/2 = z + 1.      1.      Find…

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Q: car company has $44,000 to spend on robots to put paint on new cars. There are 2 types of robots,…

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Q: Let f(x) = ln(x² + 16x + 68) f'(x) =

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Q: Typically, an inequality can have how many solutions? Multiple solutions One only solution…

A: An inequality is defined on a particular region.

Q: (a) Find a unit vector u from the point P = point Q (17, 34). = NOTE: Enter your answer in the form…

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Q: 2x²-3x + 10 dx (x²+4)2

A: The objective of the question is evaluate the indefinite integral.

Q: -5 2 y=f" (x) A description of the graph of f(x) would be: a 4th degree polynomial a downward…

A: There is a given linear graph representation of second derivative f''(x) of a function as f(x). We…

Q: VII. Let R be the shaded region below enclosed by the curves C₁ : 27(y-2) = 2(x - 1)³, C₂: x=4+√√4y…

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Q: Evaluate the integral by interpreting it in terms of areas. 4 to −9(1 − x) dx

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Q: Find the tangent plane to the equation z = 3e²²-2y at the point (4, 8, 3)

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Q: Given f(x) = x² + 4 and g(x)=√x-2. Find (fog) (x) and write the domain of (fog) (x) in interval…

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Q: ● ftan(x) sec(x) dx

A: We will use substitute method to solve the integration

Q: 5 S³ƒ( en that wer= f(x)dx 10 3 is ['f f(r)dr? what is

A: Topic :- application of integration

Q: Find the interval of convergence for the power series (-1)". Σ(−1)* (* + 2)* 13 01-1,5) O-5,1] 0…

A: The objective of the question is determine the interval in which the given power series is…

Q: Question 5 Mrs. Parkes borrowed $6000 from her friends and family and was paying them back at a rate…

A: Given data:- Mrs. Parkes borrowed money from her friends &amp; family= $6000 paying back amount =…

Q: 3 Find ( + 6x + 2) dr + C

A: To evaluate the integral.

Q: -3x²+tan(3x-5) Explain the steps you would take to find the derivative of f(x) = (e

A: Our Aim is to find the derivative of f(x)=12e-3x2+tan3x-5 -(i)

Q: How long will it take for an investment of $3000 to double in value if the interest rate is 6.5% per…

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Q: This equation is an example of which one of the following? Ax + By > C A two-variable inequality…

A: Since , x and y are variables , therefore given inequality is a  Two - variable inequality. Option…

Q: Find the partial sum S, of the geometric sequence that satisfies the given conditions. 2 a=²₁r = ₁ n…

A: Please see the below picture for detailed solution.

Q: dz Find given: dt z = xe5%, z =t", y = -1+5t dz dt Your answer should only involve the variable t

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Q: Find the exact sum of the following series (-1)-1 (0.25) 12 (0.25) 3 (0.25) 4 (0.25) 5

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