Using the trigonometric substitution x = 6 cos 0, 0 < 0 < π, the integral √36-x² x² In cos 0 + C O the above dx gives - tan 0 + 0 + C

Q: 2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following…

A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

Q: Consider the following. 2x²-3x - 5 lim X→-1 x + 1 Find the limit of the function (if it exists). (If…

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Q: Consider the following planes. 3x + 6y-z = 126 x - 12y + 2z = 0 (a) Find the angle between the two…

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Q: For the following exercises, find f(x) for each function. Use the Rule (NOT Equation 3.4 and 3.5)…

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer…

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Q: Let f(x) = (c + 1)x+ In(cos x). For what value of c is f'(/4)=6

A: This question can be solved using the concepts of differentiation.

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. (9x (9x - 8)…

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Q: Consider the function f(x) = 2x³ - 6x² – 90x + 6 on the interval [ – 5, 9]. Find the average or mean…

A: Mean value theorem

Q: 65. Evaluate ¹/2 xsin2x de

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Q: DO

A: Please refer to the image below

Q: For the following position functions s(r)=-21 an object is moving along a straight line, where f is…

A: Average velocity at t=a =s(a+h)-s(a)(a+h)-(a)=s(a+h)-s(a)h

Q: the function f: Z × Z→Z × Z defined by the formula          f(m,n) = (4m+3n, 3m+2n) is bijective.…

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Q: The gradient vector of the function f(x, y, z)= ln(yz) - x² is: 2 Select one: 0 (-2x,1,1) O None of…

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Q: Question 10 Determine the area bounded by the curves y = ex, y=x²-1, x=-1, and x = 1.

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Q: D) 5

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Q: Find the general solution of the differential equation. y(4) + 6y" + 9y = 0. NOTE: Use C₁, C2, C3,…

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Q: Evaluate the limit: lim 2-1 (5x5 - 7x) =

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. | sin (2) x²…

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Q: For a function h(x) we know that h(50)=68 and h’(50)=-5. Estimate the value of h(53)

A: Topic = Functions

Q: Find f'(x). f(x) = O O O 6x - sin² (5x) f'(x) = O f'(x) = f'(x) = f'(x) = = 6-10sin(5x)cos(5x) 2√6x…

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Q: Determine whether the vector field is conservative. F(x, y) = xe(x^2)3y(2yi + xj)   If it is, find…

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Q: Find the average rate of change for the given function over the indicated values of xx. If…

A: Given that  y = -2x2 +5x+1   where 'x' goes from -2 to 6 .     we have to find average rate of…

Q: D. f(x, y, z) = 1x + 10y + 8z Vf(x,y) =i+j+k E. f(x, y, z) = 1x² +10y² + 8₂² ▼ f(x, y, z) =i+j+k

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Q: 3x 1+x* 4. Find a power series representation for the function f(x)=; and find its interval of…

A: Please see the below picture for detailed solution.

Q: Find the general solution of the differential equation y" - 10y + 125y = 0. NOTE: Use c₁ and ce as…

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Q: Consider the following. lim 2x²-3x - 5 X→-1 x + 1 Find the limit of the function (if it exists). (If…

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Q: Write the product as a sum: 4 cos(28a)sin(18a) C

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Q: Is z=xcosϕ ?

A: To determine whether z=x cos φ.

Q: What is the integral that represents the length of the curve from x = 2 to x = 4. Select one: 0 ₂²…

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Q: Using a suitable trigonometric substitution, the integral dx 3 (16x² + 9)² is equal to sin 8+ C₁-<<…

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Q: Use the Ratio Test to determine if the series converges. 2k Σ k=1 k 149

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Q: 2. J- dx 25x9

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Q: 16 5. (a) Find the constants a,b,c for the conic r = - 5-3 cose Sketch the conic.

A: We have to find the values of a, b, c and sketch the curve.

Q: (a) Find an angle between 0 and 2π that is coterminal with 17t 10 (b) Find an angle between 0° and…

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Q: b) [ bounded 1: Find the volume of the solid obtained by rotating the region by the curve about the…

A: Graph:

Q: Question 16 Consider parts? A B -S₁²x sinx dx. Using integration by parts, let u = e2x, dv = sinx…

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Q: . (D³ - D² - 4)y = 0

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Q: Evaluate the limit of a. 3 b. O tan 2x-2sinx as x approaches to 0. c. Undefined d. Infinity

A: As per our guidelines we are supposed to answer only one question. Kindly re-post other question as…

Q: 3. Apply the root test to determine whether or not the series converges conditionally, converges…

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Q: Consider the following function and its graph. f(x): X x² + x (b) Use the graph to determine the…

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Q: Evaluate the integral with the aid of an appropriate u-substitution. Simplify the answer, if…

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Q: Question 11 Consider [x cos²x dx − x sin³x dx = = x+ƒ(x) + — 8(x) + - +C. What is the value of f 8

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Q: owing chart shows the (approximate) total number of subprime home mortgages in a state in November…

A: Please refer to the image below

Q: Use differentials to approximate to 3 decimal places ( 1.09 ) 1/3

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Q: Evaluate the given integral by making an appropriate change of variables. J 9 X - BY DA, where R is…

A: NOTE: Refresh your page if you can't see any equations. . where R is the parallelogram enclosed by…

Q: 8. Convert the angle 315° into radians.

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Q: Find the limit of the trigonometric function. (If an answer does not exist, enter DNE.) lim 8 cos x…

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Q: 27. A function on [0,2] defined by f(x) = -x² |5x – 4 4x³ - 3x (3x + 4 if x ≤ 0 if 0 < x≤ 1 1<x<2 if…

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Q: following

A: Please refer to the image below

Q: Find the constant a such that the function is continuous on the entire real line. 1 = √7x², lax - 5,…

A: Topic = Function