Find an equation of the plane containing the point (3,0,-4) and perpendicular to the line r(t)=<12-t,1-8t,4-6t > Ox-8y +6z = 27 O-x+8y +6z = -27 -x-8y-6z = 27 Onone of the above * 4 points

Q: Find the exact value of each expression by applying trig formulas (Addition and Subtraction…

A: Please see the answer below.

Q: Find the curvature and the radius of curvature at the stated point. π r(t) 10 cos(t)i + 10 sin(t)j +…

A: We are aske dto find the curvature and radius of the curve.

Q: 2x+1 x²-7x+12 S -dx

A: At first, we will do partial fraction then we will do integration

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A: I have appended the formula used in the solution part.

Q: 13. How many times will you perform integration by parts to evaluate sin(Inx) dx? A. 1 B. 2 C. 3 D.…

A: Let's find.

Q: ƒ dx = f(+ g(x)) dx, then A + f g(x) dx is equal to x³+x A. -1 B. -1 + In(5/2) C. 1 D. -1 + In(7)

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Q: af du (a) f(x, y) = sin-¹ (b) f(x, y): = x+y (c) f(x, y) = In ( t = 1 and u = 2 af and where Ət 2.…

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Q: dx If S = is solved by trigonometric substitution, which of the following x² - 2x - 4 substitutions…

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A: Theta lies  in second quadrant ot in four quadrant . First find the trig ratio considering the theta…

Q: Find T(t) and N(t) at the given point. X = = et cost, y = et sint, z=et; t = 0 T(0) = N(0) || =

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Q: Given the integral S cot³x csc5x dx. If u = cscx, then the integral can be re-written as: (a). f (u²…

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Q: - In(x - 2) + 3, X

A: answer is in next step

Q: 3) f(x, y, z)=x² + y² -2=²+ = ln(x). (1,1,1) -1/2 4) ƒ(x, y, z)=(x² + y² + =²)¯¹¹² +ln(xyz),…

A: 3)    fx,y,z=x2+y2-2z2+zlnx We have,       grad∅=∇f=i∂f∂x+j∂f∂y+k∂f∂z ∂f∂x=2x+zx ∂f∂y=2y…

Q: Σ (-1)"nx" n=1 (-1)"x" √√n n=1 00

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Q: erify the following identities: (Warning: Two-Column Proof will NOT be accepted) sin + cos 0 cot 0 =…

A: Solve as general

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A: Let's find.

Q: Sx² In²x² dx Integration by-parts

A:

Q: Find F'(x). -x+2 a. F(x) = f**(4t + 1)dt b. F(x) = ft³dt sinx c. F(x)=√ √t dt

A:

Q: Evaluate lim X→∞ ९+2 1 - x³ ( if necessary, using L'Hôpital's rule)

A: limx→∞ex21-x3Apply L-Hospital rulelimx→∞2xex2-3x2limx→∞2ex2-3x

Q: Question 6 Consider the function in the graph to the right. The function has a maximum of at x = The…

A:

Q: Given: √√-x² + 4x+5 dx. Using trigonometric substitution, what is the integral form in terms of ? A…

A: The given integral is: I=∫-x2+4x+5dx=∫9-4+4x-x2dx=∫9-4+4x-x2dx=∫9-(x-2)2dx

Q: 19. Evaluate the following sin³ [sin³ (2) cos(4) dx 32 A. 35 COS 5( 4 ) [-5cos² (4)+7] -cos 32 32 -…

A:

Q: 3) 4) f(x, y) = (xy-1)² 2 f(x, y) = √√x² + y²

A:

Q: dx secx+1

A: Given ∫dxsecx+1We do half angle substitution:=∫1tan2(x2)+11-tan2(x2)+1dxSubstitute…

Q: Using trigonometric substitution, what is A 1 6 sec-¹ (37) + √x²-9 2x² +C Ⓒ 3 sec ¹1( 3 ) + √x²³ - 9…

A:

Q: Find the radius of convergence, R, of the series. 8 n Σ (x-a)", b>0 bn n = 1 R= Find the interval,…

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Q: Use geometry to evaluate f(2x+5)dx

A:

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A:

Q: || ti + t²j||dt|

A: Explanation of the answer is as follows

Q: given: W = x² + 2y² + 2² x = cos (st) : y - 2s int 35² √+ chain role, find 3 × 502 8 using dw Ət

A: To solve the following problem

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A: Topic:- function and it's inverse

Q: Fill in the blank so that the resulting statement is true. 7x-23 If In = In (x-3), then =x-3. x + 2

A: ln7x-23x+2=lnx-3⇒7x-23x+2=x-3

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Q: Find the average rate of change of g(z) = 4x + 5 between the points (-4,-11) and (3,17)

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Q: -0.4t The rate, r, at which people get sick during an epidemic of the flu can be approximated by r…

A: Solved below.

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A: We need to describe graph of given function.

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Q: Using trigonometric substitution, what is 2 A sec-1 (3) - x²-g 6x² ® 1/1 sec - ¹ (1/3) - B x²-9 2x²…

A:

Q: I need help on number 12. Thanks!

A: 12. The given differential equation is y'-y=0  .................................. (1) We assume the…

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A:

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A: The given identity,     1+tan2xcotx=secx cscx

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A: Root test : Suppose that we have series ∑ an .Define,                 L = limn→∞ ann = limn→∞ an1n.…

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Q: c) 59 ² + √x dx x

A:

Q: X A b B a C) C D d is solved by trigonometric substitution, which of the following (b) x = √5 sec8…

A: We can solve as follows

Q: Use the Law of Sines to solve for all possible triangles that satisfy the given conditions: a = 30,…

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

Q: Calculate the derivative. f(x) = 6 - 9x¹/3 +9ex (Use symbolic notation and fractions where needed.)

A: