Convert each degrees-minutes-seconds into decimal degrees. 81) 85° 42' 18" 82) 50° 2' 15" 83) 139° 9' 0" 84) 214° 35' 42" 85) 252 0 30! 5 4!!

Q: EC an

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Q: d?y Find dr2 for the functlon: .3 3x +4x y=x

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Q: B. Determine the function which coincides with f(x) for all values with the exception x = 5. (x² - 2...

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

A: First we find radius of convergence. Then find interval of convergence. 

Q: Consider the series >. 1 1 and 1 n312 n=1 n3 + 6n n=1 Write an inequality comparing 1 1 to for n 2 1...

A: We know, n³+6n-1≥n³ for all n≥1    

Q: Find the 30th derivative of y = cos(2x). f(30)(x) =

A: Take the derivative multi times and observe the pattern then write the required answer. 

Q: 3 x2 dx 4

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Q: 3. At what points on the urve x = 2 t³, y = 1+ 4t – t² does the tangent line have slope =

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Q: cot (2x) dx . V cot2(2x) – 15 Evaluate the integral csc (2x) -Arcsec 4 A +C 4 O - - In [cor (2r) + V...

A: This question can be solved using the concept of integration by substitution and some special integr...

Q: dx S (x² – 6x + 13)² 4.

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Q: Consider the function f :R² → R given by f(x,y) = e* In(1+ y) Write down the second-order derivative...

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Q: Q2.) Graph the two equations x+y= 0 , and y = - (x -1)? ( 10 pt and find the points in which the gra...

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Q: 3. S(x) = (x²/3 – 1)²

A: Given that fx=x23-12c. if f'x>0 then function is increasing.if f'x<0 then function is decreasi...

Q: Determine whether the series converges. k=1

A: We use limit test to find convergence or divergence of given series. Follow 2nd step.

Q: If the limit of x->3- and x->3+ is +♾️, while f(3) is 2, is this a removable or infinite essential d...

A: Given

Q: Find the limit by rewriting the fraction first. ху — у — Зх + 3 lim х - 1 (x,y)>(1,4) x+1 ху — у — 3...

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Q: 7. What is dx (x six(x)?

A: Since you have asked multiple questions in a single request we would be answering only the first (7t...

Q: Find the polynomial with a leading coefficient of either 1 or - 1 and with smallest possible degree ...

A: Draw a schematic diagram of given graph.  

Q: Determine if -1 CSC if 0 1 is continuous or not at r = and 1. If it is discontinuous, identify the ...

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Q: 8-2x (f) lim- X-4 x -x-12 Vx² +16 –4 lim- (g) x' +8 lim x-2 x+2 (h)

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Q: Question Define R as the region that is bounded by the graph of the function f(x) = + 2, the x-axis,...

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Q: х — 2 1. f(x) (2? — х + 1)2

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Q: dy 2. V16 + y²

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Q: Is the series convergent or divergent? Prove in no more than two sentences. +oo 1 n=1

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Q: x²dx S: 1. 4 – 3 x' dy 2. V16 + y²

A: Let I=∫x24-x2dxI=∫x222-x2dxPut x=2sinudifferentiate dx=2cosu.duI=∫22sin2u22-22sin2u2cosu.duI=∫4sin2u...

Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

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Q: Explain briefly why the function f(x) = e" – x³ – 8 eIntermediate Value Theorem. Use IVT to show tha...

A: We will use the Intermediate value theorem. 

Q: cot (2x) Evaluate the integral - * xp- V cor (2x) - 15 csc (2x) (A) -Arcsec +C 4 (B -- In cot (2x) +...

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Q: Evaluate: lim 2 tan (r – 2) sin(x – 2)ª

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Q: Problem Set A (1) For the function f(x)=1- 1x+2 find the following: (i) f(-x) (ii) f(x +k)

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Q: Use the limit comparison test to determine whether the series converges 8. 74 +5 The series Save for...

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Q: Use any method to determine whether the series converges or diverges. (k!)° (9k)! O The series diver...

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Q: A diver launches themselves off a diving platform into a pool. The height, in metres, of the diver a...

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Q: 4 x4 differentiable at x = 4. Is f continuous at x = 4?

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Q: 2. S csch-x coth x dx

A: Given: - The indefinite integral is, ∫csch2(x)coth(x)dx To find: - The solution of the given integra...

Q: The graph shown is f(x) = sin x. What is the integral that defines the area under this line between ...

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Q: Find the tangent plane of the surface z = f(x, y) at (0,0, 0) in which 3y f(2, y) = || cos /3 t dt.

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Q: d) If the coefficients are rounded off of 0.31x + 2.73 find the absolute and relative in y x + 0,35 ...

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Q: Consider dx. Which of the following options is correct? 9+x6 1. lim Arcsin lim Arcsin 6. 6. 3 B none...

A: Given

Q: у %3D Зx5 — 15x4 + 20х3 + 3 -

A: Given : y=3x5-15x4+20x3+3   To Find : x & y- intercept of the given graph

Q: 5x² tan( 3x³) dx. If u= 3x³, then the resulting integral is Jf(u) du. Find . 5/2 A 18 5/2 18 5 18 D ...

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Q: Let F = %3| Use Stokes' Theorem to evaluate curlF · dS , where S is the hemisphere x? + y? + z² = 1...

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Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

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Q: When the numerator has a higher degree than the denominator, we have to start with long division. Af...

A: It will be covered in step 2.

Q: x²dx 1. J4 –x*

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Q: (т — 3)" - Determine the interval of convergence of 2n +1

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Q: dx Given: - 06-2x. Using u-substitution and transforming the integrand, find du. A 14e2xdx B 18e-2xd...

A: Given:  ∫dx7-9e-2x To Find: By using u‐substitution and transforming the integrand, to find du.  

Q: Given: JV5x² - 3 xdx. If we let u= 5x - 3, which of the following u-substitution formula is applicab...

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Q: Prove that the following statement is true for all positive integers. 1 1 1 + + 4 8 1 2" – 1 + 2n Pn...

A: Given; Pn : 1/2 + 1/4 +1/8 +...+1/2n =(2n -1)/2n

Q: Question 1: Differentiate the functions. 3 a) f(x) = 1– 5x +x7 b) f(x) = (x³ + 4)²

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