( 1 lim 5 X→ 2 (2) lim x x → 5 3 lim (2x+5) X→-1

Q: Differentiate r(t) = (cos(t)², sin(t)², t³).

A: The given vector valued function

Q: Use the transformation x = au and y = bu to find the area of an ellipse with equation + = 1. (Hint:…

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Q: PROBLEM No. 2. Solve the following differential equation by the method of undetermined coefficients:…

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Q: 2. Given the following tetrahedron, name the following: a. Vertices b. Edges c. Faces

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Q: Use upper and lower sums to approximate the area of the region using the given number of…

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Q: find the derivative  y=4x^2

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: For this interval notation, draw its graph and write its equality: (-∞0, 6]

A: The given interval is .The aim is to sketch the interval and write its equality.

Q: 4. A water tank in the shape of an inverted cone has height 92 cm and radius 60 cm. If the water…

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Q: Find the general solution: y" + 5y' + 5y = 0

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Q: Let f(x) = 2x + 3 and g(x) = -3x - 6. Compute the following. (a) (fog)(x) (b) (fog)(9) (c) (gof)(x)…

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Q: Solve the following non-homogeneous differential equations: x" (t) + x(t) = 2 cost 1) -X 2) y"+2y+y…

A: The given differential equation is; x2y''-2xy'+2y=xlnx

Q: If x² + xy = 10, then when x = 32 0 - 17/12 0-2 0 2/1/201 01/1/201 dy =? 2, dx

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Q: Solve the following differential equations using HOMOGENEOUS DE. Show your complete solutions. 2.…

A: To solve the following differential equation by using Homogeneous DE.

Q: Question 6: For each of the following functions f, find its natural domain. (a) f(x) = 22-2-3 (b)…

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Q: The temperature at a point (x, y) is 7(x, y), measured in degrees Celsius. A bug crawls so that its…

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Q: (2) Solve the given homogeneous equation by the appropriate substitution y dx (x + y) dy = 0. - You…

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Q: The answers for N[T(t)], t=2hr, and t=5hr are wrong.

A: Given:To find: (a) To compute .(b) To find the number of bacteria present when .Note: After seeing…

Q: The following integral is an improper integral. ( Explain why it is improper, (b) determine whether…

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Q: The radius of a right circular cone is increasing at a rate of 1.5 in/s while its height is…

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Q: Find the derivative of the algebraic function. c5-x5 c5 + x5 f'(x) = f(x) = c is a constant. X

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Q: Tel f(x) = at: *+] at x = 2

A: The given function is

Q: Isolate 9.\ 2 5 = 22 gt² + vt gt² + avt ??? 25 = 25= 2 ut(+ +2 g = expected: -avt + $25 t²

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Q: 18. Find dy/dx by implicit differentiation.

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Q: Given that f(x)= Only one item from the answer bank will be used to complete each category. Not all…

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Q: What is the difference between the disk (or washer) method and shell method? Please provide your…

A: The disk (or washer) method and the shell method are two different techniques in calculus for…

Q: A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see…

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Q: For a standard normal distribution, find: P(-1.29 Z-1.07)

A: The given probability .The aim is to find the value of the probability using the standard normal…

Q: Suppose f(x, y) = x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

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Q: A) Find the derivative of f(g(x)) at x=2  if f(2)=6, g(2)=3, f'(2)=1 and g'(2)= -2

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Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

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Q: Use the definition of e, and numerical approximations as h approaches 0 from the left, and h…

A: Use the definition of e, and numerical approximation as h approaches 0 from the left and h…

Q: y = sin-¹(6x + 1)

A: y=sin−1⁡(6x+1)

Q: Consider the curve r(t): = og(t)i + e-tj+ + 5k for t > 2. Calculate limt →+∞ r(t) (if it exists). е

A: Find the limit

Q: 7. u = (2, 2), v = (2, −2) 8. u = (2,-2), v = (−2, 2)

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Q: A 13 ft ladder is leaning against a house when its base starts to slide away. By the time the base…

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Q: 1. a = (2, 5, −4), b = (1, −2, −3) 2. a = (-1,0, 2), b = (3, 4, −5)

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Q: Differentiate the function. X f(x) = - 1 Xx +9

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Q: Solve the following non-homogeneous differential equations: 1) x"(t) + x(t) = 2 cost

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Q: 5. Let f(x, y, z) = x²e + ay³ + az + 115. Find fyzz (b) Find 8³1 əxəydy'

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Q: 8. Consider the gradph of the function f(x, y) = x² - 5xy given by z = x² - 5xy (a) ( (1,2). Find an…

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Q: Suppose that 3 J of work is needed to stretch a spring from its natural length of 34 cm to a length…

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Q: Knowing that sin(0.65) is about 0.6, find cos(0.65). What relationship between sin(0.65) and…

A: sin(0.65) = 0.6

Q: 5. Find the outward flux of the field F = xzi+yzj+k across the surface of the portion of the sphere…

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Q: Find the linear g(x) z approximation of the function given below at a = 0. g(x) = √1+x

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Q: Suppose that f(2)= -5, g(2) = 2, f '(2) = -4, and g'(2) = 1. Find h'(2). (a) h(x) = 5f(x) 3g(x)…

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Q: Let f(x) = Then f'(x) = π The equation of the tangent line to y = f(x) at a = can be written in the…

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Q: Seperate the variables and solve the equation (dy/dx)=-e^(x-y). Use the initial condition x=0; y=0…

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Q: Two sets A and B are defined as follows: A = {x, y, z); B = {1, 2, 3}. Ug Oh f range of g range of h…

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Q: If f(x) = f'(x) = ƒ'(1) = = 2 sin x 3 + cos x > 3 cos (1) () then 3 cos (x) + sin(x) (3 + cos x)² X…

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