Write a limit using summations that would equal So 0 tan (2x) dx.

Q: f (x, y) = 169 x² + y² at (-3,2).

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Q: An 8 by 8 checkerboard has alternating black and white squares. How many distinct squares, with…

A: Given: an square box in which 64 square box (black and white)

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

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Q: Use cylindrical coordinates to integrate f(x, y, z) = z over the intersection (i.e. all the volume…

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Q: Let P be the set of positive real numbers. One can show that the set P³ = {(x, y, z)|x, y, z € P}…

A: The objective of the question is determine the vector .

Q: Differentiate the following function. You do not need to simplify the derivative. 3x²e10r g'(x) =…

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Q: Find fxy(x,y) if f(x,y)= e 4xy². fxy(x,y)=

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Q: Evaluate the definite integral using Part 1 of the Fundamental Theorem of Calculus. 6² Enter the…

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Q: Enter the exact answer. tan B FREE B 55 Figure 1 4

A: Please refer attached file for solution below

Q: i) lim cos x-0 7 πCOS²x x²

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Q: Find the first four partial sums and the nth partial sum of the sequence an 2 30 an =

A: Given function is an=23n Here, we have nth term of series Evaluate the first termS1, substituting…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find each of the following when f(x) = t³d =…

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Q: tab caps lock hift ↑ esc →1 Find the first six partial sums S₁, S₂, S3, S4, S5, S6 of the sequence…

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Q: 3. Including all steps, charts, and derivations details, use the curve sketching methods to sketch…

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Q: 2. A girl of height 120 cm is walking toward a light on the ground at a speed of 0.6 m/s. Her shadow…

A: Given,            A girl of height 120 cm is walking towards a light on the ground at a speed…

Q: Consider lines L₁ and L₂. L₁: x = 1 + t, y = t₁ z = 2 + t, t€ R, L₂: x-3=y-1=z - 3 (a) Verify…

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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 area under the curve y 2 I over the interval [1, 4]

A: Find the area under the curve y=2x over the interval [1, 4]

Q: 5. The movement of the crest of a wave is modelled with the function h(t) = 0.2 cos(4t) + 0.3…

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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: 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: In the below series find the missing noumber  2 , 3, 6, 11, 20, 37, 68, 125, 230, __ , 778,1431

A: Given data:- The below series is given, 2 , 3, 6, 11, 20, 37, 68, 125, 230, __ , 778,1431

Q: 6. Determine the 19th derivative of the function y=sin(x). Fully explain the process you used to…

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Q: + y² x² + y² = 64 from x=-1 to x=-3 Find the length of arc of the curve x²

A: Given: x2+y2=64 From the limit  x=-1 to x=-3 To obtain the length  of the arc:

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: 8. Find the stationary points of the following functions and classify them as relative maxima,…

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Q: Je²² e² sin (e)dr

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Prove that the given transformation is a linear transformation - ( ) T: R³ R³; Ty = x+y+z/ + y

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Q: Find the equation of the tangent to the curve y = sin(3x) COS(z) at z = 4.

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Q: (a) Consider the power series Show that B(x) converges for all x. B(x) = Σ n=0 (-1)η 2η 22n (n!) ²

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Q: find the area of the region enclosed by the curve defined by y=x^(2) -2x-15 and the x-axis. Please…

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Q: The following factors correspond to which one of the following equations: (x + 1) (x - 6)? x^2 + 7x…

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Q: Let f(x) = f'(x) = f'(9) = 4log7 (x)

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

A: Topic = Sequence

Q: x² yey lim(x,y)→(0,0) x4 + x + y²

A: To evaluate the following limit.limx, y→0, 0 x2yeyx4+x+y4

Q: 1 f(x) =(√² + √2)²

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Q: A lamp post 3m high is 6m from a wall. A man 2m tall is walking directly from  the post toward the…

A: Given:- The given lamp post 3m high is 6m from a wall The given man's height is 2m The man is…

Q: Find the nth term of a sequence whose first several terms are given. 10 11 9' 10' 11' 12' an = Need…

A: The given sequence is 89,910,1011,1112,....

Q: The slope at any point on a curve is given by 6x-2. Determine the equation of the curve it passes…

A: Slope of the curve is given by dy/dx

Q: For the curve given by the vvf r(t) = ti + 2t²j+t³k, find the unit tangent T(t), principal normal…

A: I have appended the formula used in the solution part of the question

Q: Find the gradient of f(r, h) = 2ärh + ár² at (6,3). NOTE: Enter the exact answer.

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Q: Find the general antiderivative of f(x) = = + C -28²³-03-2/3 + √²

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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: Convert x2+y2= 26 to an equation in polar coordinates in terms of ? and ?.

A: The given equation is x2+y2=26 we have to convert this equation into polar coordinate in terms of r…

Q: Find the first five terms of the sequence. 011/5 82=1/25 83 1/125 841/625 85 1/3125 50 Determine…

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Q: 17. f"(6) and f" (a) $(0) = (0) ³+4 (6) ³ + 2 Ans: f(0) = 2 for Problems 18-20 use the following…

A: Question : for problems 18-20 use the following graph. 18 . Largest open interval from where…

Q: Let f(x) = ln(x² + 2x + 6) f'(x) =

A: We have to find the derivative.

Q: Q-3: a) b). Using logarithmic differentiation, find the derivative of -3x√2x-5 (6-5x)4 - 34x = 0.…

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Q: 6) 3/2 · 4x²)³/; 9x dx

A: Our Aim is to solve the integral given below:-∫9-4x252x6dx -(i)

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: We have to find the area between the curves.