5. Let f (x) = a sin b (x- c). Given that a, b and c are positive, find the value of a, of b and of c. 2n -1 -2

Q: Given that cos(x) = (-1x2 for e<xc than a powr saries of cas(x) %3D ie e (2n)!

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Q: 37. ; with r = 1 andh = ;: 0, p2 sin¬! V1-h² /r²-h/r2-n? (0,, 33 47-3/3 (0, 0.71)

A: Let's simplify in steps Let's take the numerator first:

Q: If sin' 0+y cos e sin e cos e and x sin e = y cos 6, prove that x + y* = 1.

A: Solution

Q: Determine fry when f (x, y) = x sin¬' () -1 1. fry = (x² – y?)3/2 y? x² – y? 2. fry - xy 3. fry (x²…

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Q: 2. If f(x, y)=x² sin y-y cos.x-xe - ye" +5x°y°, show that ô²f _ ô²ƒ ôxôy ôyôx

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Q: | Suppose f(x, y) = 2 sin(11ry) and g(x, Y, z) = /144 – x² – y² – z². Find the following function…

A: Guven, f(x,y) = 2sin(11xy) f(9, pi/72) = ?

Q: 29 - For what values of a and b is | S x+3a-b axt 26 3x-5 Continuows at every X?

A: g(x)=ax+2bx≤0x2+3a-b0&lt;x≤23x-5x&gt;2

Q: 2. (a) Let f(x, y) = x² sin(x + y), find 잃 and 잃.

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Q: 1. If y= tan x, prove that y"= 2(y² +1)(3y² +1).

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Q: Complete the following argument that sinx#x for any x in the interval (0,1): • For any x in (0, 1),…

A: 1) the mean value theorem . 2) c . 3) is greater than . 4) is greater than .

Q: 1 If z = 2x2 – 3y with u = x² sin y and v = 2y cos x, determine expressions %3D az dz for and du

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Q: Q1\ Differentiate the following (choose two only) 1)z = sin (3x + 1) 2)f (x) = 3cot-12t 3)y = e 8*…

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Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is f'(pi/4)=4

A: sol:-    Given f(x) = (x+ln(cosx)  differentiating ω. r.t   x, we get    f1(x) = c+1cosx(-sin x)…

Q: Suppose that S"(ax + b) cos x dx then the value of a equals

A: Given,           ∫0πax+bcosxdx=6To find: The value of a.

Q: The integral / 2/ (*) cos(2*) dx takes the form k cosu du when u=2* and f (x) =x – 5. what is the…

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Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

Q: 1. If y= tan x, prove that y``= 2(y² +1)(3y² +1).

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Q: B. and , if z = (x² + y²)³/2, and r = e-" sin v, y = e¬u cos v. В. %3D

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Q: Compute and * for the equation sin(x)e +2z²y = cos(z). 4xz COS ду

A: sinxe4xz + 2z2y = cosz∂z∂x = ?∂z∂y = ?   While calculating ∂z∂x  variable y will be considered as…

Q: 1 dy sin¬' x If y = xv1 – x² + sin=1 x, prove that 24 – 2

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Q: 6. If f(x, y, z) = r³y³ sin (z²)+z³ cos (r³), find an expression for fryz and evaluate it at the…

A: x, y and z are the variables of function f Differentiating partially the function f with respect a…

Q: Q2- Show that, 2 sin x |Jo(x cos 0) cos 0 d0

A: We have to prove sinxx=∫0π2J0(xcosθ)cosθdθ                     (1) Since we know…

Q: If f(x,y,z)=In(x²y+sin² 12

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Q: 4. Differentiate the following. Justify ever (i) f(x) = (2x + 1)³(5x² + 4) (iii) sin(cos x)

A: Given function is: fx=2x+135x2+4 Differentiating f(x) with respect to x we get,…

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); u =

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Q: Given that: z = y sin(2x) + (1+x²)e* + cos x tan¬1(y* + 1) In(y6 + 137)

A: z=ysin2x+1+x2ex+cosxtan-1y4+1lny6+137 Differentiating wrt x, we have…

Q: 4) If F(x)= } d, then F'(x)- sin t

A: Note : According To our guidelines we can solve only first question and rest can be reposted.Thank…

Q: 3. If v = sin- (4) + tan-' (±), find the value of r + y. 4. If z= ear+by. f(ax – by), prove that b…

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); U =

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Q: 5. If z = f(x, y), where x = r cos 0 and r sin 0, find z and and hence show that: (). (-(( 2 2 dz dz…

A: To find the partial derivatives of the following function in two variables by chain rule.

Q: (22 – 2) | Evaluate dx 2+2 (x4+5x2 +4) tan1 2 A - BI E E E E X O Type here to search 马

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Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: 7. Let f(x,y)= a) T 2 xsin y-y, find sin x+y Simplify and give exact value

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Q9: If F(x, y, 2) = [sinh-(sin- (In (/sin(cos(x²)) y? + zyx + y, find and ду az Q10: If z =…

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Q: The integral / 2' )cos(2*) dx takes the form k cosu du when u=2* and f (x) =x- 5. What is the value…

A: we use the formula ddx(ax)=ax lna

Q: Given f(x,y,z) = sin (2xy) + 5xyz3. Find fyzy(3,2,4).

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Q: D. 1. If (x + y)² = x² + y² 2. If y = sin³ () cos³ () dy - dx X prove that y' = sin² (x) cos(x) 8…

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Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

Q: Differentiate the following using the Chain Rule: 2. H( X)= ( 2X+4)³ 3. h(x)= (3x-4)? 4. x (x)= 2…

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Q: (2 2.) If f(x) = 2x 1 and p(x) cos (x). Find x, for 0≤x≤ 2π, if (f op)(x) = -2

A: Hi! Thank you for your question.As per guidelines we can solve one question at a time in case of…

Q: 2 Given that: J2(x)=-, cos.x + sinx find J(x)

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Q: 22: Find dyldx for the following functions * (40 marks) · y = In (3 – 4 cos x) + (4x – 5)5 2. y = x²…

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i 5 .5 и 3

A: The function is given by  fx, y = sin8x-5y The point is x, y = 5, 8 The unit vector is  u = 35i-45j…

Q: If y = (x – a)/2ax – x² + a² sin¬'(÷ prove that y' = 2/2ax – x² a is constant.

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Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. @ y(x)…

A: We find the general solution of given DE  y"+y'=-cos(x)........(1)

Q: 1 Evaluate the equation /o x² sin (xy)dydx

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Q: (f) If w=4x² +4y² +z² ,x= p sinø cos0, y= psinøsin0 , z =pcosø, Əw find and ap

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Q: 6. If x= sect and y=tant, evaluate at t =- of the following: dy (a) dx d'y (b) dx?

A: x = sect y = tant

Q: If f(x, y) = e“ sin(4y) then: 4 sin (4) 4 cos( 4) V f( – 1, 1) . el el

A:

Q: 2. Is it possible to write sin (37x) as a linear combination of sin(2rx) and sin(Tx) for all values…

A: