7. Prove: cos(0 + 2) 7) = sine.

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A: Given that y= √(2x) and x= 2 and we find equation of tangent line and normal line at the given…

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A: Here we have to find the sum.

Q: Solve the following equation on the interval 0 ≤0<2T. cos ²0- - sin ²0= sin 0+1 Select the correct…

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Q: Consider the function f(x) = 12x5 + 15x¹ - 240x³ +2. f(x) has inflection points at (reading from…

A: Consider the function fx=12x5+15x4-240x3+2.fx has inflection points at reading from the left to…

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Q: Use the Integral Test to determine the convergence or divergence of the following series, or state…

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A: y if the equation defines y as a function of z but not vice versa, x if the equation defines z as a…

Q: verges. 8 (-1)"6" n=1 5n lect the correct answer below: a) The series converges absolutely O b) The…

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Q: Find the volume of a pyramid with height 29 and rectangular base with dimensions 6 and 9 using…

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Q: When you evaluate: A B D B C None of the given choices E RIN 2 SST xsin ²(y) dy dx the results is 0…

A: The given double  integral is xSin2y, y from 0 to pi, x from 0 to 2.

Q: Use the Laplace transform to solve the following initial value problem: y" - 6y +9y=0 y(0) = 5, y(0)…

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Q: n Use the comparison test to determine if the series n=1n²³+²+1 converges or diverges.

A: The given series is ∑n=1∞nn3+n+1 we have to find the series is converges or diverges, by using…

Q: Question 3 dz Find the partial derivative for the function z = 20y²√x. dy C ay az ay N GE - 201 az =…

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Q: Q5. (a) (i) (b) (c) (ii) Express sin 2x Express cos 2x Show that in terms of in terms of sin x Solve…

A: Given problem:- (a) (i) Express  sin 2x in terms of sin x and cos X.(ii)  Express cos 2x in terms of…

Q: Consider the function f(x) = 12x5 + 15x¹ - 240x³ +2. f(x) has inflection points at (reading from…

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Q: Determine the explicit formula for the n-th term of the sequence written below. Note that the first…

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

Q: Draw the directional field for the differential equation. y' = y2 − 1   What can you say about the…

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Q: -6 (Click on graph to enlarge) What is the Domain? What is the Range? 1,0 intonal notation

A: We have to find the domain and range of the given graph.

Q: Consider the function f(x) = 2√x+1 on the interval [4, 7]. Find the average or mean slope o the…

A: We will find the required.

Q: Which of the following is a nonhomogeneous A. (x-1)y"-xy' + y = 0 C. D³ (D²-4)y=3x+2e-3x linear…

A: Non-homogenous differential equations : If the differential equation have a function on the…

Q: Solve: -95A + 20B = 40 -20A- 95B = -190

A: given that  solve, -95A+20B=40 -20A-95B=-190

Q: On which of the following intervals is the function g(x)=e-200x² concave down? ○ (-5,5) ○ (5,6) (6,…

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Q: Use the Comparison Test to determine whether the series converges. Σ k = 1 1 5k5 +6

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Q: In *In ecot³x dx feln sinx

A: We need to evaluate integral.

Q: dx 4+9х2-6х

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Q: If f(3) = 5 and f ′(x) ≥ 2 for 3 ≤ x ≤ 7, how small can f(7) possibly be?

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Q: Determine whether the telescoping series converges or diverges. 5 5 Σn=1 (√2+2 -√2+3) /n+2 a) The…

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Q: Roughly 12,000 people in a certain country are diagnosed with thyroid cancer every year, which…

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Q: If a population of is becoming extinct and the population is decaying exponentially. Assume that…

A: From given information

Q: Determine the volume of the solid formed by revolving the area bounded by x² + y² =25 and x + y = 5…

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Q: dy Find the complete solution of 2 + 4y = 1 dx

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Q: Find the area of the region in the first quadrant bounded above by y = -x² + 6 and below by y = x. 4…

A: Solution of given question is written in below steps.

Q: 1- Find the inverse of Laplace transform of log s²+1 (s-1)²,

A: To find inverse Laplace transform:

Q: Find the area between the graph of x = 2y + 3 and the y-axis on the interval [0, 2]. 4- 3- 2- 1…

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Q: Find the directional derivative of the function at P in the direction of v. √2 2 f(x, y) = x³ - y³,…

A: Given problem:- Find the directional derivative of fx,y=x3-y3 at point P8,3 in the direction of…

Q: g(x) = cos ¹x+ 1-x

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Q: Determine whether or not the relation is a function and then give its domain and range in interval…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A: This question can be solved using the concept of parametric and symmetric equation of lines in three…

Q: 17 prove 4 Cos" ☺ - Sin" 0 = Cos20

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Q: Find the radius and interval of convergence of the power series (−1)″ (x+2)" √n.3n n=1

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Q: Find the area of the surface generated when the given curve is revolved about the x-axis. 3 1 + 6 2x…

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Q: Question For the following graph of a function, estimate the area under the curve on the interval…

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Q: dX If the side of a cube is expanding at the rate d = 2t cm/sec, and X(0) = 3 cm. What is the volume…

A: This question can be solved using the concept of differential equation.

Q: Determine the area bounded by y²=x+4 and x-2y+1=0 A B E 27 - 2 32 - 3 27 - 5 sq. u. 34 5 sq.u. sq.u.…

A: y2 = x +4  x- 2y +1 = 0 for find the area bound by this curve  we have to find common point of curve…

Q: Using the Limit Comparison Test with the geometric series -17, to 8 67 determine if the series given…

A: Limit comparison test -  If we have two series ∑n=1∞an and ∑n=1∞ bn and limn→∞(an/bn) is finite and…

Q: Use an appropriate substitution to integrate Jaco 24xcos (x²-2) dx

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Q: A region bounded by fly) = y + 1, y = 4, and x = 1 is shown below. Find the volume of the solid…

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Q: It is a fact that the function  f(x) =  (9x2 − 2) (4x2 + 4)  has a limiting value. Use a table of…

A: We need to find limiting value.