If A' = g;a,rsys , Yi = birx, , and a;,b,j = dij. Find A' in terms of the x,

Q: If --kr, show that d? dr %3D dt

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Q: Solve the following first-order linear DE's. y' + (cotx)y = xcscx, y = 1

A: we have to find the general solution

Q: Find the first and second deriva tives sp dt

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Q: Let b(x)=h' (x), find the tangent line to b(x) when x = 6 .

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Q: Led xe R be such thad Xn→x, show that %3D

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Q: If the tangent line to y=f(x) at (4,3) passes through the point ( 0,2) , find f(4) ,f  '(4)

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Q: Let C be the shortest path that connects a to ni and / S (sinhz + 1)dz. Then %3D

A: Given :I=∫c (sin hz+1)dz, where c is path fromπ to  πi We need some hyperbolic formulas, cos…

Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

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Q: Given show =5 how dy %3D

A: differentiate y with respect to x .

Q: find the value of tangent LA. C 12

A: we know that tangent A =tan Afrom ∆ABCtan A=BCAC

Q: Show that S, (In x)? dx = e – 2

A: The detailed solution is as follows below:

Q: In lam(플 + )1-men dy is dz et y

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Q: Again differentiate with sespect do 'x get we A cost- B Sinz A cosz + BSiny) { from @ d +

A: Please refer the attached image for complete solution.

Q: If b is dviisible by a (a|b) and b in different than 0 then |a| is less or equal than |b|

A: The given statement means the following.

Q: If UV = 7, UX = 5, and XY is x + 3 find x. Assume that segments %3D that appear tangent are tangent.…

A: Given circle is as below :

Q: 1)cotx will be cont 0) is

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Q: Find an equation of the tangent line to the curve y = (In 3) 3* at the point (0, 1) y = (In 3)²x + 1…

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Q: Let (a, b) be an arbitrary point on the graph of y = 1/x, x > 0. Prove that the area of the…

A: The given function for the curve is, y=1x The slope (m) of the tangent at the curve is,…

Q: ove that 1 cosh(tanh) = -1 -1 < r < 1. V1- 2

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Q: isfies the differ and the auxi

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Q: What is tanh (Ei) O V3 V3i O 13

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Q: O Deltarentiatk with respect () Singe (X+1) (x-)

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Q: Let C be the shortest path that connects à to ni and I = S. (sinhz +1)dz. Then

A: Integration of hyperbolic function ∫sinh(x) dx=cosh(x)+C Now, in the given problem to determine…

Q: If u= In x, then 1- (In x)2 dx=?

A: Find your answer below

Q: a, given that the line ax+y+1 = 0 is tangent to the grapl

A: We have to find the value of a according to the given information

Q: he coefficient ao of Fou +2 t. く?

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Q: If z =e* + In(xy) Evaluate- ,and ,at the point (1, 2). Hence, calculate the change in z when x…

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Q: Let z = 6exv , find dz %3D

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Q: If UV = 7, UX = 4, and XY is x + 2 find x. Assume that segments %3D that appear tangent are tangent.…

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Q: Find the equation of the tangent plane to z = In(x³ + 1) + yª at the point (0,3, 81).

A: We have to find equation of tangent plane at (0,3,81).

Q: If the tangent line to y = f(x) at (3, 2) passes through the point (0, 1), find (3) and r(3). (3) =…

A: In this question, we need to find f(3) and f'(3).

Q: J Ax) dx 11. 12. -3

A: 11) From 0 to 5 there is a trapezium and from 5 to 6 there is a triangle

Q: The ________ ________ is derived from the Pythagorean Theorem.

A: We know that, The distance formula is derived from the Pythagorean theorem.

Q: Compute sec? z + x) dr

A: Given : ∫12sec2x + xdx

Q: Let C be the shortest path that connects n to ni and I = S. (sinhz + 1)dz. Then

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Q: ind the iquation of a tangent line of to the graph of at the pont (2, f).

A: Let's find.

Q: a) In exercise 1.1, describe the erro statement of the tangent ratio.

A: Given : The statement, Figure :

Q: Suppose you Know that tand 3/12. Vsing this infe, de tevmine cuhot quadiantdis in dnd Caliulate…

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Q: 1. use O D with tangent As and AM'. 20° 35° M а. тzGMН H A b. MLAEM E 70° S 125° B,

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Q: Find the tangent of ZU. V11 12 U V

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Q: If u In x, then 1-(In x)2 dx =?

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Q: Show that the line y = mx + b is its own tangent line at any point (x0, mx0 + b).

A: Given:Show that the line y = mx + b is its own tangent line at any point (x0, mx0 + b).

Q: Find the tangent plane to the equation 3y cos(5x – 4y) at the point (4,5,15)

A: z=3y cos5x-4y Let, Fx,y,z=3y cos5x-4y-z=0  ......(1) Now,  Fx=∂Fx,y,z∂x=-3y sin5x-4yx5-0…

Q: pes of animals are treated by at least on r. Scott, and Dr. Baker)?

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Q: tan What is the exact value of sc wdw ialuulexalu fXis thrali

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Q: "ind the orthogonal compliment to S = span{

A: Here we have to find the,

Q: The slope of the tangent line to the graph of y = In(ry) at the point (e, 1) is

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Q: Find all values of x where tangent lines to y=x^5 and y=x^6 are parallel.

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.