Example 19: (a) If x +y = 25, find dy/dx. (b) Find an equation of the tangent to the circle x +y = 25 at the point (3, 4). Solution: (a) Differentiate both sides of the equation x + y = 25

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A:    limn→∞ arctannnlimx→afxgx=limx→afxlimx→agx,   limx→agx≠0=limn→∞ arctannlimn→∞ n=π2∞ Apply Infinit...

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A: Take LCM of the right hand side and the put x= 1

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Q: Case 4: repeated quadratic factor (very hard!) 8dx • Example 1: r(r2+2)2

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Q: VAT4 : then what is dy2 x+4 dx dy а. 4x(x +4) dx dy 4Vx +8 dy = 8 Vx + 4 b. dx C. dx dy d. dx 4(x + ...

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A: Solving the problem by finding the limit of the function.   NOTE :: As per our Expert guidelines we ...

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Q: Use the square configuration to complete the algebra rule: (a + b)? = a- a+b OUT - - b ----

A: We know that algebraic rule is : (a + b)2 = a2 + b2 + 2(a.b)   Here i attached the solution of this ...

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A: According to bartelby guidelines i am supposed to answer only 37.-3-9i5-8ion rationalization we get-...

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

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A: Given: y=32x-92         asymptote 1 to hyperbola                                         1y=-32x -32...

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A: Here, given that f is continuous for a≤x≤b and differentiable for a&lt;x&lt;b.

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A: Given f(x) =3x²-2  And g(x)=1-f(x) =1-(3x²-2) =1-3x²+2 g(x)=-3x²+3 For slope of curve g(x) different...

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A: We can write the given equation as:  1-231-121-13-613x1x2x3=7-313 The coefficient matrix is: A=1-231...

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Q: Find ((dy)/(dx)) if y is a differentiable function of x and x^5+3y^4=x^5 tan y + 10

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Q: Case 3: non-repeate quadratic factor (x²-x-21) Example 1: S 2x3-x2+8x-4

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Q: ii. find the equation of the tangent line to f at x = a. (a) f(x)=3-4x, a=2. (b) ƒ(x)=x² +x, a = 2.

A: We have to determine the equation of tangent line 

Q: Evaluate the following integrals. Express the final answer in its simplest form and without negative...

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Q: Find the Maclaurin polynomials of orders n = 0,1,2,3, and 4, and then find the nth Maclaurin polynom...

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Q: 1. f(x) = x2 + x – 1 for all values of x %3D

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Q: If f(r, v)= +y-2y, find fa (2, 1), f (2, 1), fay(2, 1) and fy(2, 1).

A: Given a function f(x,y)= x3+x2y3-2y2 Now, fxx= ∂2f∂x2=∂∂x∂f∂x fyy= ∂2f∂y2=∂∂y∂f∂y fxy=fyx=∂2f∂x∂y=∂∂...

Q: Find projy u. v = 7i-3j+ k, u = -4 j+ 3 k 60 45 j+ k 59 59 O 105 i- 59 45 15 k 59 59 9 9. +k

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Q: Find the limits of the functions below a) limr-3 x* sin x b) lim,

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