-6 Evaluate , (2x + V) dx. A. 27 + 2/3 + 4/6 B. 27 2/3 C. 27 23 4V6 D. 27 + 4v6

Q: ) = x/x² + 36 ned on the interval – 4 < x < 5. ) is concave down on the interval x = to x = ) is…

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Q: Sketch the graph of the function f(x) = x³ – 2x² – 5x + 6 using calculus – based analysis. -

A: Given problem:- Sketch the graph of the function f(x) = x3 – 2x2 − 5x + - 6 using calculus - based…

Q: t"(x) If t(x) = Vx find t'(x)' O -1/2x O 2x 1/2x -2x O None of these

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Q: For the graph of f(x) = x-7x² -6x +5, find the value(s) of x for which the tangent to the curve is…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

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Q: 19. What is the seсond derivative of y бх* - 3x1 + х2 -57 а. у 24х1 — 9х2 + 2х b. у"3 144х — 18 с.…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj -st

A: Plot the given vector Fx,y=xi+3yj.

Q: 3 Find the slope of the tangent to the graph of f(x) = /x+5 at the point where x= 4.

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Q: ,3 dx 3 Vx²-16

A: Given integral I=∫x3x2-163 dx

Q: Let a be a real number and f(x, y) = 3ax?y + 6xy3. Let v = 3i – j and let V f(r, y) denote the…

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Q: The sum of digits of integer x is y . the sum of digits of y is z. find x if x+y+z = 60 step by…

A: Here we know that x,y,z are two-digit numbers since their sum is 60 and any two-digit number can be…

Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = t'i + tốj K(t) =

A: We can solve as follows

Q: If f(x) = 2 g(x) find g'(x) in terms of f'(x). O g'(x) = f(x)/2 O g'(x) = 2 f(x) O None of these O…

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Q: Given the function f(x) = x2 and the closed interval [0, 1, which of the following is a value of c…

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Q: Find div F and curl F if F(x, y, z) = 10e*Y i – 6 cos yj+ 2 sin? z z k. div F= curl F=

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Q: Given the function g(x) 6x + 63x² + 216x, find the first derivative, g'(x). = (x),6 Notice that…

A: We use second derivative test to determine the local Maxima and minima

Q: A tank is being filled with a liquid. Z (1), given below, is the amount of liquid in liters in the…

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Q: What is the area of the region bounded by the graph of r = 4 cos 0? %3D Choose two (2) correct…

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Q: Evaluate

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Q: Sx³e*²dx 3. X°e

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Q: (y – x) dx + 15x?y? dy

A: answer is in next step

Q: What is the radius of curvature at point (1, 2) of the curve 4x – y2 = 0.

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Q: Suppose the function f(x) is an odd function and lim, f(r) = 27. Use this information to evaluate…

A: For an odd function f(-x) = -f(x)

Q: Calculate the area enclosed by the f(x) = x3 – 6x² + 8x and the x-axis. curve

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Q: Find the volume oF the solid that results when the region enclosed by the give N curves y=e ソ=o, ×=…

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Q: D If the Taylor series expansion for f (x) is given by f(x) = Eo- (x- 2)*, then f(4) (2) = %3D

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Q: Consider the function f(x) = 9x + 4x-1. For this function there are four important intervals: (- 00,…

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Q: k S = (d – 2)? where c and k are positive constants which depend on the quantity of smoke each stack…

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Q: _4. What is the first derivative of f(x) = (x² – 4)(3x – 2)? а. 9х? - 4х — 12 b. (2х)(3) C. 6x d. (x…

A: Topic:- derivatives

Q: ||r'(t) x r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = 8 cos(8t)i+8 sin(8t)j+ 5tk…

A: The given formula is: κt=r't×r''tr't3 And rt=8cos8ti+8sin8tj+5tk

Q: Problem 37: Convert the following complex numbers from rectangular form to polar form: a. 4+ j3 b.…

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Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)

A: This is a problem related to vector calculus. Based on green's theorem we will solve the integral.

Q: What is the volume of the solid formed by revolving the region bounded by the graphs of x2 = 9y and…

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Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the…

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Q: Let S1 be the hemisphere with Cartesian equation z = 6 – /36 – x² – y? and S2 be the upper nappe of…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 5 cos(t)i+11 sin(t)j+4tk;…

A: Given problem:- Find the curvature and the radius of curvature at the stated point.   r(t) = 5cos…

Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y'x²j+ 2z²yk. %3D div F= curl F=

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Q: Consider the following functions. f(x) 3 Vx - 3 g(x) = x – 3 %3D Sketch the region bounded by the…

A: Let us first find the intersecting point. So,               x-33=x-3⇒x-3=x3-9x2+27x-27⇒x=2, x=3, x=4…

Q: Find curl (8z i + 9x j + 8y k). curl (8z i + 9x j + 8y k) = ( i )i + ( i )j + ( i )k

A: We know: Where P, Q and R correspond to the components of a given vector field:F→=Pi→+Qj→+Rk→ curl…

Q: Let 7 (t) = < 5t? + 5, tª + 3t, In a. Determine the coordinates of the point on the curve traced out…

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Q: Consider the function f(x) = 2x° – 15x? – 36x + 8 on the interval [– 5, 9]. Find the average or mean…

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Q: a/a + b/b 189 a/b + b/a = 180 Find a and b value

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Q: 8. c d 12 10 values of the areas bounded by the curve h', the derivative of h, and the x-axis on the…

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Q: A stone is thrown vertically upwards, from the edge of a 5 m tall cliff with an initial velocity of…

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Q: 2 Determine the equation of the tangent line to the graph of f(x) = Vx-12x at the point where x -3.

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Q: Consider the following equations. f(x) = x5 + 3 %3D g(x) x + 3 %3D

A: The region is bounded by the graphs,  fx=x5+3 and gx=x+3

Q: ||r'(t) × r"(t)|| ||r"(t)||* Use the formula k(t) = to find k(t). r(t) = t²i + t°j %3D K(t) =

A: Given: r(t) = t2i +t5j Solution: r'(t) =ddtt2i+t5j =2t i +5t4j r"(t) =ddt2t i +5t4j= 2i + 20t3j

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: View Policies Current Attempt in Progress Find curl (6z i + 7x j + 9y k). curl (6z i + 7x j + 9y k)…

A: Solution:

Q: Given f (x) = x³ + x² + x + 1 and its derivative f'(x) = 3x² + 2x + 1, find the equation of the…

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