csc ² 5x cot 5x dx, can be evaluated conveniently using Trigonometric Transformation. A True B) False

Q: 1. S(5x4 + 2x – 1)dx

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Q: 3. Determine the following a A negative angle in radian measure coterminal to Show calculation steps…

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Q: Q2) Solve the D.E xdy + (2y – x4 + 3x)dx = 0

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Q: Convert to an equation in rectangular coordinates. r = 4 csc (0) – sec (0) (Express numbers in exact…

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Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series…

A: For radius and interval of convergence we will first findlimn→∞an+1an then equate it to <1 and…

Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

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Q: rln 2 e2" sec-'(e²)dx 0.

A: Answer is in below steps.

Q: dy Which of the following is the general solution of the separable equation, = = 2y - 1? dx in 2y-1|…

A: Solving the problem by finding the differential equation. Here we take C as integral constant.

Q: an = In(n+1) – In(n) for n E N determine if the following is convergent or diverge An

A: limn→∞an=limn→∞ ln(n+1)-ln(n)=limn→∞ lnn+1n=limn→∞ lnn(1+1n)n

Q: 1.5 3-X Evaluate the integral *dy dx using polar coordinate

A: Follow the procedure given below.

Q: Determine whether the following functions below is a solution or not a solution of the integral f(1-…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i+4 sin(t)j+ tk;…

A: Answer in the box are correct

Q: (a).x = 61, y = - 4 + 7t O (r, y) = (0,4) + «(6, 7) ai + bj = 4j + 1(6i + 7j) O (1, y) = (6, 7) +…

A: topic - equation of a line

Q: Find the Taylor series generated by f at x a. 1 f(x) = , a= 1 x2 Choose the correct answer for the…

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Q: Let g be a differentiable function of x, and let the range of g be an interval [a, b]. Let f be a…

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Q: Find an equation of the plane through (4, 1, –4) that is perpendicular to the line x – 2 = 5t, y+3 =…

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Q: (-3)"(x – 2)" Consider the power series Vn+2 Use Alternating Series Test to show that the series…

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Q: Write each complex number in complex polar notation: 21) - 4.053 +2.042.

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Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

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Q: Consider the following function. f"(x) = 48x Find f'(x). (Use C for the constant of the first…

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Q: dy_ 1-y dx V1-x? V1-x' +/1-y? = a(x - y), then show that %3D

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Q: The graph of the function fis given. y 32 24 y fx) 16 8. 8. 16 24 32 40 48 (a) Use six rectangles to…

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Q: Find f"(1) if Ax) = X+1. %3D 1 1 1/4 12 OOO

A: To find f'1 if fx=xx+1.

Q: Find the absolute extrema of the function on the closed interval. h(s) = [0, 2] S-3 minimum (s, h) =…

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Q: Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 9…

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Q: Question For the function given below, which statements concerning Rolle's theorem are true? 4x + 3…

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Q: f(x) – f(2) x - 2 Find the difference quotient when f(x) = 2 + 4x + 5x². Simplify the expression…

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Q: 1/x ,2 xp -0-

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Q: Use the limit definition to compute the derivative of the function f(t) = , at t = -4. (Use symbolic…

A: This question can be solved using the concept of limit definition of derivative and equation of…

Q: In 4x 5. S dx

A: The integration of the integral is ln(4x)/x.

Q: Let f : [a, b] R be a continuous function on [a, b). Prove that if |f(x)| dx = 0 then f(r) = 0 for…

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Q: Solve if the improper integral below diverges or converges. If it converges, solve for the value. 1…

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Q: Question Using Rolle's theorem for the following function, find all values c in the given interval…

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Q: Find f'(1) if Aæ) = (x² –-x²-x+1)(x² + 1). 1 O 2 O -3

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Q: (-1)" V2n2 + 5 n er series (x + 1)" n=1

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Q: n(x – 2)" 3" (2n – 1)3 * VI. Consider the power series > n=1 a. Show that the power series converges…

A: Solving

Q: 18. Find the shaded area in the following figure. Assume that there are infinitely many squares and…

A: Area of Infinite shaded region Let Sk be the sum of area of each shaded regionthen…

Q: (-1)" Given: power series (x + 1)" 2n2 + 5 n=1 ii. Find the interval of convergence of the power…

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Q: /2n?

A: The given series is: ∑n=1∞(-1)n(-1)n2n2+5=∑n=1∞(-1)2nn2+5n2=∑n=1∞1n2+5n2

Q: 8. Find f(x) dx if for x < 4 f(x) = for x 2 4

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Q: Find f"(-1) if Ax) = (x² -x+1)(x +1). O -1 3. O -3 9.

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Q: xdx S- can be solved by either algebraic subsitution or integrataion by parts. X-1 A True B) False

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Q: Q3) Evaluate triple integral , dz dx dy.

A: We can calculate this as follows:

Q: Find the equation of the tangent line to y = 7e* at x = 3. (Use symbolic notation and fractions…

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Q: Evaluate the limit, if it exists: x²-9 lim *-3 X+ 3 does not exist -6 1

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Q: Suppose you decide to wait 5 years to save up before buying the house.  You are able to put a down…

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Q: Find the Maclaurin series of the function. f(x) = 9 cos 2TX 2 (Type an expression using n and x as…

A: We know that the Maclaurin series of the function f(x) is given by f(x) = f(0) + f'(0)1!x +…

Q: A rectangular piece of cardboard has a size of 45 x 24 cm. This cardboard will be made into a box…

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Q: Find the derivative/s of the given item. Final answer should be simplified. dy Find dx if yvx – 8 =…

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