Calculuate the length of the curvey = 4√2 3 3|2 within the interval of 0≤x≤ 1,

Q: . The voltage,V, in a circuit is slowly dropping at a rate of -0.01 volt/sec as the battery wears…

A: I have appended the formula used in the solution part.

Q: * Evaluate. [12 [20x cos(5x² - 1)]dx

A: The given integral is   ∫20xcos5x2-1 dx We solve the integral using proper substitution .

Q: Question 2 Consider the equation: 2²-11-12 A) First, use the "completing the square" process to…

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Q: Using trigonometric substitution to solve: f 1 A + C 8 sec x√4-sin2x sin 2x + C 4 cos x√4-sin²x sin…

A: Solution is given below:

Q: Explain why you think the sequence converges to a finite number or n+1 diverges. If the sequence…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Calculate the first, second, and third derivatives of 9 y(x) = 48 + x (Use symbolic notation and…

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Q: Sπ/4 ___xª dx (x²+4)5/2 (Use trigonometric substitution)

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Q: quotient (Express numbers in exact form. Use symbolic notation and fractions where needed.)…

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

Q: B 0 Consider the integral f sin-¹x dx. If we let u = sin ¹x and dv = dx, the integral can be written…

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Q: Using integration by parts, Then k is? (a)-1.5136 [²x³ cos(x²) dx = k - [*²x sin(x²) dx (b)-1.1365…

A: Our Aim is to find the value of k by evaluating the integral using integrationby parts.∫02 x3 cos…

Q: Explain why you think the sequence converges to a finite number or (n+1)! diverges. If the sequence…

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Q: Question 3 3x² + 5x + 2 Let f(x) 2x² + 71 4 This function has: 1) A y-intercept at the point 2)…

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Q: List intervals on which the following function is INCREASING. Use INF for infinity, use no spaces,…

A: The given function,    fx=3x2-1

Q: Given: (1+2x) ex dx. Using integration by parts and letting u = − 1 − 2x, dv = f(x)dx, then the…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Integration by Parts 4. fxe4x dx 5. [ e* cosx dx

A: This question can be solved using the concept of integration by parts.

Q: Evaluate Ic (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (9, -7)

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Q: F(x) = integrate (3t + 2) dt from 2 to x + 2.  Use  first fundamental theorem of calculus to find…

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Q: mby f(x) = (lnx) (sin x). The figure above

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Q: /² sin sin ( π/4 x² dx (x²+4)5/2 (Use trigonometric substitution) fe2x+Inx² sin x² dx = = Find f…

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Q: Question 4 15x²x³43x - 19 The integral (x + 1)²(x² - 6x +13) Ax + B What is the value of ax²+bx+c²…

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Q: 1 2x²-3 √² ²3 dx = (x² + 3)² + ²x² ³ + d x+√√x²+3 27 x²

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Q: a. Find the volume of the solid obtained by rotating the region bounded by y = x³, y = 8, and x = 0…

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Q: Find the area of region bounded by the graphs of the equations. 1. y = 5x² + 2, x = 0, x = 2, y = 0

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Q: -π/4 x3 dx (x²+4)5/2 (Use trigonometric substitution)

A: We have to solve above question useing trigonometry substitution

Q: 0 X State in words all the transformations necessary to obtain the graph of y=2f(x-2) from the given…

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Q: Using trigonometric substitution, what is A 1 6 sec-¹ (37) + √x²-9 2x² +C Ⓒ 3 sec ¹1( 3 ) + √x²³ - 9…

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Q: Water is dripping into a hemispherical bowl with a radius of 8 cm at a rate of 1 cubic cm per…

A: Volume is evaluated.

Q: Explain why you think the sequence 1-(-1)" con converges to a finite number or n+1 diverges. If the…

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Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: Write an equation for a function that has a graph with the given characteristics. The shape of y =…

A: We can find the correct answer as below.

Q: tan6(x) cos4(x) sin²(x)sec³(x) [7sin²(x) + 9cos²(x)] + C A 63 tan²(x) [7tan²(x) +9] + C B 36 Ⓒ…

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Q: Use the formula (t) k(t): ||r' (t) x r"(t)|| = 13 ||r' (t)||³ r(t) = e¹²ti + e-tj = to find k(t).

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Q: You have found an annuity that will pay 4.75% annually and you plan to put $1,000 into the annuity…

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Q: Given the integral S cot³x csc5x dx. If u = cscx, then the integral can be re-written as: (a). f (u²…

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Q: = Consider the integral f sin-¹x dx. If we let u = sin¯¹x and dv dx, the integral. can be written as…

A: Explained below

Q: Use the method of Lagrange multipliers to maximize the function subject to the given constraint.…

A: we have to find the point (x, y)

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: We need to find domain and value of r(t).

Q: Solve the differential equation: * (D² - 3D + 2)y= 2e-x + 8

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Q: Find all real solutions of the equation 8m² -18-374. Write your answers as a list, using a comma to…

A: A detailed solution is given below

Q: The Leaning Tower of Pisa in Italy is 181 ft tall and makes an angle of 86° with the ground. A…

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Q: Find the inverse of f(x) f-¹(z) = . ✓ 3z + 1 -3x+4

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Q: √ 1 x²√2x-x² dx = x+¹√ √√2x-x² + c 3x²

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Q: Question 10 Terry is skiing down a steep hill. Terry's elevation, E(t), in feet after t seconds is…

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Q: domain of the function: A = 8 B = and C= 8 For each of the following intervals, tell whether f'(x)…

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Q: dx 1-x² -2

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Q: f(x, y) = 3x² - y x4 x² + 2y ² 1 (x, y) = (0,0) 2 D (X,Y)= (0,0) 1 Determine if f is continuous at…

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Q: Given The boundary of C: 0 ≤ x ≤ π,0 ≤ y ≤ sinx With Green's Theorem, Evaluate this line integral. $…

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Q: 2. Show that the series is conditionally convergent. n=2 cos(nx) √n ln n

A: Solution of the problem as follows