State both forms of the Chain Rule for calculating the derivative of y = f(g(x)). State both forms of the Chain Rule. dy d dx dx (g(x))) =|

Q: x+5 9 – (x – 3)²

A: Given: I=∫x+59-x-32dx    ....(1)   We know the trigonometric identities; (1). sin2x+cos2x=1 (2). cos...

Q: 2. f(х, у) 3 а? —гу + у? then ,is

A: Given: fx,y=x2-xy+y2   We know that; The sum/difference rule: f±g'=f'±g' The Power law; ddxxn=nxn-1 ...

Q: Practice Pg)48 on increasing expontntial fonction 4=al6y and foncti on gu=<(d)Y interseed a de creas...

A: Explained below 

Q: Find the first derivative of 2cos(2 + x³). a. -6x² sin(2 + x³) b. -x² (sin 2 + x³) c. -6x² (cos ...

A: daf(x)dx=adf(x)dx ; where , 'a' is constant. dcos (ax)dx =-a.sin(ax) dxndx=n.xn-1 . 

Q: Find the integral of sin^8 xdx from x = π/2 to x = 2π  a. 0.814 b. 1.289 c. 0.240 d. 0.365

A: We have to find  the integral of sin8 xdx from x = π/2 to x = 2π 

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Q: Calculate sin r e at a 10 to get 15 correct significant digits. What is the 14th digit? Answer:

A: Given expression is: sinx-x We have to calculate it at x=10-6.

Q: ch of the following sequences. Always justify your ans 1+ncos(2m) sin n+ c - In с) а, d) а, 2n 3 n°

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Q: 3x dx 1+r4

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Q: Sketch the region bounded by the given curves, then find its area. x = y^2, x = y + 6

A: The graph is shown below in which the chex region represent the area.

Q: L:x = 2 – t, y = 3 + 4t, L2: x = 4t, y = 1 – 16t, z = 4 – 8t z = 4 + 2t

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Q: Given the curve ax? = y³, find the shortest possible distance between the curve and the point (0,8a)...

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

Q: 13. A cylindrical can is to be made to hold 1.5 L of oil. Find the dimensions that will minimize the...

A: This is a problem related to maxima and minima of the function. Based on the general formula we will...

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Q: 180; 수i1 Question 8 Find the length and direction (when defined) of u × v. u = 4i + 2j + 8k, v = -i ...

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Q: 4. What is the volume of the prism? 4.6 in 5.1 in 2.1 in 13.6 in 2.8 in

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Q: 00 Σ The population of a country dropped from 51.6 million in 1995 to 45.5 million in 2009 Assume th...

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Q: from the observer? Remember the sides of a right triangle are related by 20 s saigt foward an obsenv...

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Q: conditions for each equation: d²x 2 dx (a) + x = 1 dt F(0) = F'(0) = 0 %3D %3D dt2

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Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| = ...

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Q: Determine whether the following series is convergent or divergent: (4n)2n evnn2n n=1

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Q: Find the area bounded by y = 2 -x squared and y = x A 9/2 7/2 5/2 3/2

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Q: Given the function notation f (x) = x2 – x – 4. Find the value of x when f (x) = 8

A: Given the function notation f (x) = x2 – x – 4. Find the value of x when f (x) = 8

Q: e*Vex-1dx ex+3

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Q: S sin(bx) sec(bx) tan(bx) dx

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Q: A chemical substance has a decay rate of 9.5% per day The rate of change of an amount N of the chemi...

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Q: Find the critical points c for the function f and apply the Second Derivative Test (if possible) to ...

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Q: Consider the following. u = -9i – 4j – 2k, v = 4j + 4k (a) Find the projection of u onto v. (b) Find...

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Q: (2y – 3x)dx +xdy = 0 %3D

A: Find your answer below 

Q: 6. On a certain workday, the rate, in tons per hour, at which unprocessed gravel arrives at a gravel...

A: 6) Given that the rate in tons per hour at which unprocessed gravel arrives at a gravel processing p...

Q: solve the integral: integral from negative infinity to positive infinity [ (1)/(4x2 + 4x + 5) ] dx

A: The given integral is ∫-∞∞14x2+4x+5dx we find the value of the integral using proper substitution.

Q: Find the vector component of v = 2i – j+ 3k along b = 4i + 4j + 7k and the vector component of v ort...

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Q: Show that the functions in Exercises 21-28 have exactly one zero in the given interval. 21. f(x) = x...

A: Given problem:- Show that the functions  have exactly one zero in the given interval 21. f(x) = x4 +...

Q: Find a formula for the nth term of the sequence. - 2, 1, 6, 13, 22, ... Determine the sequence's for...

A: We have to find the sequence's formula in terms of n. 

Q: With

A: As per the guidelines we can solve 3 parts only. 

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A: We have to find solution of given expression.

Q: 2n + 1 n -1 n tan n=1

A: Find the limit of the given equation at infinity.

Q: By using the substitution u = x3n, find nx3n-1, 'e*" (e*™ + 8) dx where n is a constant. Hence, eval...

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Q: Find the vector component of v = (4, – 1,7) along b = (3, 6, –6) and the vector component of v ortho...

A: We can solve the given problem as follows:

Q: .... a) What percentage buy the game without seeing a TV ad (x = 0)? 19% (Type an integer or a decim...

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Q: (3.x (За — 1)" 5" Vn +1 n=1

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Q: Question 8 Find the derivative of the function at Po in the direction of f(x, y) = 3x 2 + 4y, P o(8,...

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Q: Consider the parallelepiped with adjacent edges u = 8i + 7j + k v = i+j+ 2k w = i + 8j + 5k Find the...

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Q: Parametrize the line that passes through the point (1,2,3) parallel to the vector v = -3i + 7k.

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Q: 1.f(0) = (금x* + 3)" %3D

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

A: We have to find w vector for given condation.