Differentiate the function. 1 f(x) = In .4 %3D f'(x) = %3D

Q: If f(x)=3x^2-2, and g(x)=f−1(x), what is the slope of the curve g(x)=f−1(x) at the point (10, 2)

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...

Q: For each of the following matrices, either find its inverse or say how you know it isn't invertible....

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Q: dx x-1

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

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Q: If y = sin (4x - 5), then what is y' a. y = 4 cos (4x - 5) b. y 3 сos (4x - 5) C. y' = -cos (4x) d. ...

A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to d...

Q: Wrat is the equation in standard form of ahyperbola whose asymptotes are y=- うオー and y= -x- and a ve...

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

Q: Using the method of Lagrange multiplier, determine the minimum and maximum values of f(x,y,z)=2x+3y ...

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Q: Principal Compounded semiannually The principal represents an amount of money deposited in a savings...

A: Given table:- Principal Rate compounded  Time $ 6000 8℅ semiannually 5 years   To find:- The...

Q: Ve dx is convergent or Determine if divergent. Evaluate if convergent. x2

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Q: Find the indefinite integral: 30 [cos 3x + sin 2x + e5x]dx 10sin 3x -20 cos 2x +6 e5x + C O 90sin 3x...

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Q: If ƒ is continuous for a < x < b and differentiable for a < x < b , which of the following could be ...

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

Q: Find all the first order partial derivatives for the following function. f(x, y) %3D хуе "У af dy af...

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Q: Find dy/dx. No need to simplify. With explanation

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Q: Find the interval of convergence of 5 (x - 8)" In (9n) n=2 (Use symbolic notation and fractions wher...

A: Radius of convergence of a series of the form ∑n=0∞an(x-a)n is given  by R=limn→∞anan+1and then inte...

Q: Let 8 be a twice-differentiable function with g'(x) > 0 and g"(x) > 0 for all real numbers x, such t...

A: We have to find g(6) 

Q: Find the interval of convergence for the given series. 2(n + 3)!(x + 13)* Select the correct respons...

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Q: Graph the integrand and use known area formulas to evaluate the integral: dx

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Q: A given partial fraction Cx +D x² +1 2x A + X+4 (x-1)(x+4)(x² +1) X-a A can be evaluated as: O 15 2/...

A: Given that partial fraction 2xx-1x+4x2+1=Ax-1+Bx+4+Cx+Dx2+1To find : value of ASolution:2xx-1x+4x2+1...

Q: Find the radius of convergence and the interval of convergence. k(k + 1) k=1

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Q: Prove: If the characteristic equation of ay" + by' + cy = 0

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Q: ind the equation of the osculating circle at x=2 for y= 1/4x^2-x. Draw the circle

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Q: Find the first, second, and the third derivatives of the following functions: f(x) = (-x* + 4) . -4x...

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the quest...

Q: Evaluate the following limits, if they exist, by using the graph 3 -4 -2 1 -1 -2 -3 -4 a) lim_ f(x) ...

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

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Q: 2ea dx (ет — 1)2 1

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Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. nk - 1 k> 2 ...

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Q: Given f(x,y) = x3y-3xy³. Evaluate fdy O 14y-27y + C 6. O -6y³ +8y/3+ C бх2 - O 6x2 – 45x + C 4 2x2 –...

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Q: Question 2 tan (0) Insec(0) do A -Incos (0) + C 2 B - (Insin(@)) ² + C - (Intan( @)) ² + C D (Insec(...

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Q: Directions: Evaluate the following. Show ALL necessary solutions. x³+2x²-1 1. lim x--2 5-3x 2. lim v...

A: In this question we have to find the limits. Note: As per our policy we are suppose to do only 1st t...

Q: Use sigma notation to write the Maclaurin series for the function. 2sin Ax 2(-1)'+1 (2k + 1)! k-D0

A: Given function is f(x)=2sin(πx) Use Sigma notation to write the maclaurin series of the given functi...

Q: find u*v where theta is the angle between u and v. llull=4, lvl=16, theta=2pi/3

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Q: Find the derivative of the vector function below r(x ) = sin (secx 2)i +csc°(Vx² +1)j +8tan(x")k 1 A...

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Q: Find the indicated vector. Let u = (-1, -1), v = (7, S). Find u + v. O (-8, -9) O (7, 6) (6, 7) O (2...

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Q: Find F'(x) if F(x)= e^(-x^2) * x^sin(x^3)  Use logarithmic differentiation

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Q: Find the particular solution to the following equation y" + 4y' + 5y = 0 y(0) = 1; y'(0) = -3 Hint: ...

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Q: curve in the xy-plane is denned by the vector valued functic dy in terms of t? dx? where x(t) = 2 ln...

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Q: Find all the second order partial derivatives of the given function. f(x, y) = cos (xy 2) - y2 sin x...

A: In this question, we need to find all the second order partial derivatives of the given function.

Q: The region bounded by f(x) = - 4x2 + 20x + 96, x = 0, and y = 0 is rotated about the y-axis. Find %3...

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Q: Let m(t) be a function with the values given in the table below. 1 t 2 3 m(t) | 100 1600 25600 40960...

A: topic - exponential function

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 ...

Q: 1. A movie theater seats 240 people. For any particular show, the amount of money the theater makes ...

A: The given that the number of people in attendance is given by: n=240-12p...(1)  where the price of a...

Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*...

A: We can answer all three subparts as below.

Q: Explain if the function is continuous or not for the given number a. if x > 1 f(x) = {1 if x = 1 ,a=...

A: topic - limits and continuity

Q: A- Use the fixed point and Newton-Raphson methods to estimate the root of the function, employing to...

A: We have to find Root of the function by both methods. 

Q: termine the critical points of the function f(x,y)=-2xy + y –x'. fter olessifir uhother 2ngh orition...

A: Please refer to the image below 

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

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Q: Let m(t) be a function with the values given in the table below. t 1 2 3 m(t) | 100 | 1600 | 25600 |...

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Q: 0 sin x

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Q: sin(0) Evaluate: lim 0→る

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Q: Find the magnitude of u x v and the unit vector parallel to u x v in the direction of u x v. u = 2 i...

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