43. Calculate F'(0), where x° + x* + 4x – 7x F(x) x4 – 3x² + 2x +1 Hint: Do not calculate F'(x). Instead, write F(x) = f(x)/g(x) and express F' (0) directly in terms of f (0), f'(0), g(0), g'(0).

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A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

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A: Solution:

Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

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Q: Q3) Find dy/dx if 1- y= In x 2- y=x sinx+1-x

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Q: If z = +3y, find the differential dz. dz =

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A: To Determine: find the fourth derivative of the function .  Given: we have a function…

Q: solve the differenhal equa hon by varianon of parameters y" + 3y't 2y 7 te* y (x)

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Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

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Q: 4. Show that 2 s w (b) L(t sinh (wt)) (s² – w²)2 -

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Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: 8) Find the linearization of f(x) = 6 + X+1 tan 4 dt at x = 0. 1.

A: On solving this we will get

Q: In(x), Sn (4t + et) dt. Find the derivative of F(x). 3.

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Q: Suppose y = square root 2x + 1 where x and y function of t . A) if dx/dt =12 , find dy/dt. When x= 4…

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Q: - ((x3 + x)sech(In x)) = dx EX)-

A: To find  ddx(x3+x)(sech(ln x) We use product rule  d(uv)=udv+vdu Let  u=x3+x,     v=sech(ln…

Q: 6. Find the first order derivative with respect to z of the function u = In/x2 + y2 +z²

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Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

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Q: tan(3x + 8). Let y : Find the differential dy when x = 5 and dx = 0.4 Find the differential dy when…

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Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

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A: Given that,  x2+y2=64

Q: 4. Compute the second derivative with respect to x of 3x³ + 8 y : at x = 1.

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Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…

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Q: 1- Solve the second derivative forf(x, y,z) = e sinay3) əx2

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Q: tan(4x + 8). Find the differential dy when x = Let y 1 and dæx 0.3 Find the differential dy when x =…

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Q: 4. Show in two ways that the function f(z) = exp(z²2) is entire. What is its derivative? Ans. f'(z)…

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Q: 1. Solve the first derivative of f(x) = e-2x In x at x = 0.5 using forward finite-divided difference…

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Q: The derivative of y= sech1(Inx)+esinh(3x) equals Select one: 1 3e sinh"(3x) O y' = - xInx/1-Inx…

A: Proceed as shown below...

Q: Calculate differential: f(x) = e-* cos(3x) + 2 of the range [1,2] with h=0.05 Using the backward…

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Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

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Q: In(4z+10) Find the derivative of the function f(z) = z'sin(9z + 12) + %3|

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Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used:…

Q: 15 - What is the approximate derivative of f(x) = 5x³ + 4x² if we use f(ze+h)–f(za) forward…

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Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

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Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

Q: In (3x) Find the derivative of y with respect to x if y = sin (7 e') dt. %3D dy dx

A: Given y=∫0ln3xsin7etdt.We need to find dydx

Q: If f(x) = A B tanx 1+e 1+1² 1+e¹ In (secx) √ 1+tan²x 1+ e tanx sec 3x tanx -dt, then f'(x) equals

A: solution:-f(x)=∫0tanx1+t21+etdtApplying leibniz integral…

Q: (1) Suppose that y is a function of r satisfying the equation 5x + 10y + 3.ry+ 5y + 6x 0. Use the…

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