dx. J x² + 2x + 5 x+1 11 arctan x+1 11 ;+ 2x – In [/r² + 2x + S- *+ 2x + In Vx? + 2x +5+, arctan 2 2 O Option 4 Option 2 11 x+1 – In Vr² + 2x + 5 + arctan 11 x+1 - 2x – In |/x² + 2x + 5 + arctan 2 2 2 2 Option 3 Option 1

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A: We have to find maximum value of the directional derivative at the given point.

Q: x(x + 8)(x – 2) and f"(x) = (x + 3)³ x3 – 4x? 8(7x – 4) Given: f(x) = · with f'(x) = (x + 2)2 (x +…

A: Given: f(x)=x3-4x2(x+2)2f'(x)=x(x+8)(x-2)(x+2)3f''(x)=8(7x-4)(x+2)4

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Q: Explain why S is not a basis for M, O sis inearly dependent. O s does not span M.2 O sis linearly…

A: We can solve this as follows:

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A: Mass= density× volume

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A: Topic = Derivative As per guidelines , At  a time only one question can be answered out of different…

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Q: Find an equation of the plane that passes through the point P(-8, –4, 7) and has the vector n = (-2,…

A: Given problem:- Find an equation of the plane that passes through the point P(-8, -4,7) and has the…

Q: 1.

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Q: Suppose f( – 1) =7, f'(– 1) = 4 , and g(x) = r°f(x). The tangent line to g(r) at z = 1 is given by Y…

A: Given: gx=x3fx, f-1=7, f'-1=4   The expression for the equation of the tangent line is: y-y0=mx-x0…

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Q: The sum of two numbers is 12. if one number is x, what is the value of x such that the product of…

A: Here, let the two numbers be: x & y Then, x+y=12⇒y=12-x Now, the product of the two numbers be:…

Q: If L is a line in 2-space or 3-space that passes through the points A an B, then the distance from a…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: Solution is given below

Q: Find the arc length in the second quadrant of the curve x23 +y2/3 = 25 from x = - 125 to x = – 8.…

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Q: Example 2.35: Using Implicit Differentiation to Find a Second Derivative d'y dx Find if x +y² = 25.

A: Explanation of the answer is as follows

Q: Identify the open intervals where the function is changing as requested. Increasing 3 45 6 O (-3,…

A: Increasing

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Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y+3…

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Q: Evaluate * (1 – x²)3/2° 1 + c 3 1-x2 -1 + c /1 – x² O Option 4 Option 2 2 1 1 + c /1 – x² :+c 3 V1-…

A: ∫ xdx/(1-x2)3/2 here assume that  1-x2 = u -2x = du/dx xdx = -du/2 ∫ -du/2u3/2 ∫ -u-3/2du/2 2u-1/2/2…

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Q: 4x+10 J (x-2)(x²-2x+1)

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Q: Verify that the two planes are parallel. -x + 6y + 22 = B -글x+ 3y + z =9 Find the normal vector, n,…

A: I have appended the formula used in the solution part.

Q: The sum of 2 numbers is 15. Find these numbers if their product is a maximum

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Q: Question 2 of 10 View Policies Current Attempt in Progress Find the directional derivative of f at…

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Q: 7458 B2 Follow the solution format on the picture.

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Q: Given that dx = m. a) Find [g(x) – 8] - 8] dx. [Select ] b) Find 3g(x - - 3) dx. [Select] | g(x) da…

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (– 10,…

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Q: 6. The sequence (xn) = (3,3,3,3, ...) is .. a) not Cauchy b) unbounded c) divergent d) convergent

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Q: 10 40 What does that mean 11 Suppose f(x)dx : f(x)dx is equal to? 10

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Q: х3+9х2+20х 4. lim х-3+ х2+x-12

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Q: Write the equation in spherical coordinates. (a) z? = x² + y² (b) x² + z² = 9

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Q: +t, 2t +t, 6t} O sis a basis of P O sis not a basis of P3.

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Q: Solve the differential equation with the appropriate method. Finalize the answer equated to y. 1.…

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Q: State whether the following numbers are rational or irrational. a) V4+7/2 b) V36 c) V112510716

A: Given: a)4+72b)236c)112510716

Q: Find the volume x=y-y2; x=0 revolving at y-axis

A: Given problem:- Find the volume x=y-y2 ; x=0 revolving at y-axis

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Q: Determine the interval(s) on which the function is continuous: 2r+ 7 212-3x-9 if x 1/2 Ox1/2 Ox1/2…

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Q: Si sin“ (3y) cos® (3y) dy 128 2340135 128 780045 O 9.64 x 10 4 O 2.89 x 10 3

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

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Q: Determine whether the sets S, and S, span the same subspace of R. s = ((0, 0, 1). (0, 1, 1), (8, 1,…

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Q: Use the chain rule to find dy/dx for th following (a) y= (3x^2 - 13)^3

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Q: Vx* Show that for x > 1, coshx-(cosh 3x- sinh? 3r dx 3x) In(x+ Vx² (b) )= In(x+ Vx .2 +Vx -1

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Q: 32 3.

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