Solve each of the definite integrals in Exercises 67–76. 37 sin° x dx | sin° xdx 67. 68. 8, /2 69. cosxdx 70. | sin? x dx -1/2 sin x cos?x dx | sin? x cos?x dx 71. 72. T/4 /2 sec*x tan? x dx cscx cot³ x dx T/4 73. 74. 0, 14 sin² x | cos" x /4 sinx dx cos?x 75. dx 76. 0.

Q: Calculate without using a calculator log2(25/3)

A: log2(253)

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Q: The power series 1+2 (x+9) +3 (z + 9)² +4 (x + 9)"+ is centered at O z= 9 O I= 0 O I=1 O I= -9

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Q: 2)The radius of a sphere decreases at the rate of 4 m/sec. Find the rate at which the volume decreas...

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A: Given integral, ∫x+22dx5-4x-x2

Q: 59. Show that for any number a > 1 -Ina In x dx + e dy = a In a,

A: Given: ∫1alnxdx+∫0lnaeydy=alna

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Q: Using the integration by parts once, the integral (In x)2019 dx becomes A. x In x- x + C B. 2019 In ...

A:  integral given,∫lnx2019dxLet us substitute  t=lnx                     then x=et                    ...

Q: What can be said about f(3) if f is continuous and lim f(x) = ?

A: We know that a function f is said to be continuous at x = c if limx→cfx=fc.

Q: Let z = 3 -i and w = -2 – 2v3i . Evaluate . O a. V3 3n (3n +isin ) cos w Ob. V3 +isin () cos V3 (cos...

A: we will use following identities to evaluate given expression  a+jb = a2+b2 ∠ tan-1ba and A∠θ1B∠θ2 =...

Q: 11. Define what it means for a sequence {ak} to be eventuallystrictly increasing.

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Q: Evaluate the double integral : 2 2 (3 x² + 4 y°) dx dy Answer: 2 2 (3 x2 + 4 y) dæ dy =

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Q: Summarize limits of three special functions below. a. lim sint а. lim t-0 t 1-cost b. lim t-0 et-1 с...

A: (a) To find: The limit limt→0sin tt. Calculation: The limit limt→0sin tt is in the form of 00, Apply...

Q: 17

A: Given, fx=x+10  on 0, 8 with n=30

Q: Find the positive values of p for which the series converges. (Enter your answer using interval nota...

A: See the attachment

Q: q6

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Q: Determine the one-sided limits numerically or graphically. If infinite, state whether the one-sided ...

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Q: 1. If f(x, y)=3x' sin y- y² cos x- 2yln x– xh y- 4xy , find- of ôf ô²ƒ ô²ƒ

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A: Satisfied all hypothesis of mean value theorem

Q: If tan A =n tan B and sin A = m sin B, prove that cos A = m -1 n-1

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Q: c. lim_sin x x- a. lim sin x %3D

A: We know that for any given functiony=fx, at x=a limit will exist if limx→a-fx=limx→a+fx

Q: Example 4: A water trough is 10 m long and a cross section has the shape of isosceles trapezoid as s...

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Q: Explain the method of proving the derivative (dy/dx) of sinh(x) and cosh(x) ?

A: Given That: The hyperbolic functions sinh(x)  and cosh(x)

Q: In Problem, and are given.Find the exact value of each of the four remaining trigonometric functions...

A: In Problem, and are given.Find the exact value of each of the four remaining trigonometric functions...

Q: Classify the discontinuity of as a removable, jump or infinite?

A: This question is related to continuity and differentiability.

Q: 81. Consider the function f(x) = x cos 2r. (a) Find the signed area between the graph of f(x) and th...

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Q: The half-life of radium is 1690 years. If 10 grams is present now, how much will be present in 50 ye...

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Q: If f(x) = x^2-7x+8 find f(2)

A: We have a quadratic form of a  function. The general form of a quadratic function is  fx=ax2=bx+c , ...

Q: discuss the determining limits using L hopitals rules with an example?

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Q: Answer the following CALCULUS problem:

A: Given, f(x)=sinx

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Q: 10. (D² – 6D + 9)y = e3x

A: Given, D2-6D+9y=e3x To solve the above differential equation.

Q: snip

A: For solving the given equation following properties of logarithm will be used. One property that wil...

Q: 3. DETAILS Consider the following integral 3d.x V(16 + 4x2)5 A suitable trigonometric substitution t...

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Q: (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a ...

A: Given: The function y=cos3x and the point π4, -22, To determine: The equation of the tangent to the ...

Q: Express dw/ðr and ðw/ðs in terms of r and s if w = z² + y°, x =r – s, y=r +8.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Consider the region enclosed by the curves y = I+1 and y=2x+ 1: %3D

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Q: If P(z) = z3 + qz – 52 and z =-2 – 3i is one of the solutions of P(z), which of the following is cor...

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Q: DETAILS The area bounded by y= , the r-axis and the line r = -1 and r= 4 is equal to %3D %3D 17 A. 4...

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Q: Determine whether the integral is convergent or divergent. 1 dz z2 + 3z + 2 convergent divergent If ...

A: ∫0∞1z2+3z+2dz

Q: 1. Construct the table of values for f(x) = In x . Start by approaching the number 1 from the left o...

A: Use the calculator to find the each value in the table than check the limit at x = 1

Q: I need help

A: see 2nd step.

Q: x+1 Find S dx. [Hint: Rules of integration and Trigonometry substitution] 9+x²

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Q: In Problem, sinθ and cos θ are given.Find the exact value of each of the four remaining trigonometri...

A: Given: sinθ=45  ,cosθ=-35

Q: Explain the method of proving the derivative (dy/dx) of sinh(x) and cosh(x) ?

A: As we know sinhx=ex-e-x2 and coshx=ex+e-x2 Then, ddxsinhx=ddxex-e-x2=12ddxex-e-x=12ex+e-x=coshx Ther...

Q: QUESTION 3 Let x2+y4 x²+4y4 f(x,y)=- be given. Which of the following is TRUE for this function? lim...

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Q: In the given question ,, two models R1 and R2 are given for revenue (in millions of dollars) for a c...

A: Given: Two models of revenue for a corporation which are estimates of revenues from 2020 through 202...

Q: 64. Use the method of completing the square and what we know about transformations of graphs to prov...

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Q: b) Find the total area between the region and the x- axis. y= x – 4x ; -2<x<2

A: Given equation is                    y=x4-4x