R and r are defined by E(; - 1)(y, – I) VE(*; - 1)² E(Y SSR Sry S,, Syy R? TY r = SST' (1) Show R2 = r2.

Q: c. - f'(1) = (3e³ – 2p¹³) In (5p¯² — *√p) -

A: To differentiate the given expression f′(1)=3e3−2p−1/3ln(5p−2−p−1/4), we'll need to apply the chain…

Q: d Evaluate the following derivative: dx (1 + t² dt. Oxv1 +x4 + v1+x² Main Content None of these O…

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Q: 8. which from the following is function but not one to one O ys = x° + 8 O y' = x6 + 3 O {(2, 9) ,…

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Q: A r&r.'Find y as a function of t if 9y" – 24y' + 7y = 0, and y(5) = 3, y' (5) = 8.

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Q: 16. The value of y' for y = x³ + 2x² – 4 at point (-2, –4) is, I. -4 П. 4 III. 6 IV. 8 | II O IV

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Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

Q: of of and dy 6. For the function f(x.y) = sin ° (6x - 5y), find of df dy II

A: In partial derivative when take the derivative with respect to one variable consider other variables…

Q: showo haw [co(t)+ 3sine) ]= vioet coslt- antan( 3)

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Q: Find any inflection points for ?(?) = ? 3 − 3? 2 + 1 Use f

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Q: What is the coefficient of x2y' in (5x- y)?

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Q: The domain of y = is A. (-0,00) B. (0,00) C. (-∞,0) D. x + 0 E. x + 1

A: Solution: The domain of a function is the set of input or argument values for which the function is…

Q: For which values of r is the function y =t" a solution of t?y" – 5ty' + 8y = 0 Select one: O a. r=…

A: Given differential equation is euler-couchy homogeneous differential equation which can be solved by…

Q: Which of the following is y' for the implicitly defined function æ²y = 5? Oy' = -2x Oy' = -2xx' -2y…

A: Given that: x2y=5

Q: If y = xsin then y is equal to = X" at x =

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Q: Let g(8) = (2s – 1)°. Then g'(8) is 9'(1) is 9'"(8) is and g''(1) is

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Q: Q1/ If z = f(x, y) and z* - y? = 6x²y°z7 Find: and dz

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Q: 8. For the function y = e* + sinx: a. Determine y', y",y",y^),y(5), y(6). b. Describe the pattern…

A: We have to find the differentiations of the give function and find y101.

Q: OL. If w = f(u, v), u = cosx and v = sinx, show that: (30 Marks) %3D d?w dr v² fau + u?f- 2uvfuv -…

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Q: For cos2(xy) =, evaluate y' when x = 4

A: Given that: cos2(xy)=14

Q: 16. Find the values of r so that the function y= e™ satisfies the equation y" – 4y' – 21y = 0. A)…

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Q: In 2020, the pandemic caused by COVID-19 has created havoc all around the world. In a small island…

A: Number of people residing in the island: 1200000 Number of infections per day: 30 Total number of…

Q: B) If f(x.y) x'y? +x*y , find: axdy *Əyər

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Q: hup lict funcrion F(xig) = x?y -eto =0 P(e, 1) Find y" (e) = ?

A: Here to use implicit diffrentiation method for solving the problem

Q: Ex. 4) For F and G functions and given that: F(5) =-1,F'(5) =-3 G(5) = 4 G'(5) = 2 a) If P(x)= F(x)·…

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Q: Q.5: Derive reduction formula of f cot"x dx. Also prove that -cot*x cot2x S cotx dx = + InSinx + C.…

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Q: (4x³y*)² (2x?y-)° (6xy ³)³

A: The given expression is 4x3y-222x2y-506xy-33 Use the property amn=amn and a0=1 to get:…

Q: Find the first derivative of y= (a - Va? + æ O a. (2 4 + 8x*) 8. 49V6 (等 )+ (等 ) (等-+) O b. 2/ 7.…

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Q: If r(t) 0, show that r(t) = r(t) · r'(t). ‡

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Q: 3. _1ffx,y) = tan—1 (), then X c) (x2 +y2)2 is ܐܐܐ )b ܐ)?x +y(

A: The given function is fx,y=tan-1yx. Find the value of ∂f∂y. Here we use the following formulas -…

Q: Jack drives east away from Hilltop bakery at 60 mph while Jill drives toward the bakery at 40 mph…

A: Given that,

Q: y? lim (х.у)-(1,0) х2 + у? — 2х + 1

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Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: Suppose f, g have the following values: f(3) = e5 and g(3) = 2. ƒ'(3) 10 and g' (3) = = 8. 4 Let y¹…

A: To find the value of y' at (3,-3).