Mensuration of 3D shapes: Shape Cube Cuboid Sphere Volume (Cubic units) a³ lxbxh (4/3) πt r³ Curved Surface Area (CSA) or Lateral Surface Total Surface Area (TSA) Area (LSA) (Square units) (Square units) LSA = 4 a² LSA = 2h(l+b) 4πr² 6 a² 2 (lb +bh +hl) 4 πtr²

Q: The height of a projectile launched into the air is given by f(t)= - 16t2 +97t+9, where t is the…

A: Topic- Average rate of range of function over interval we are given f(t)=-16t2+97t+9Average rate of…

Q: Discuss the continuity of the function. x² - 4 x + 2 f(x) = f is discontinuous at x =

A: Given, f(x)=x2-4x+2

Q: D DETERMINE IF THE FUNCTION IS EVEN, ODD, OR NEITHER SHOW JUSTIFICATION. x-1 5x − 7 x²-3 x² +6 y=…

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Q: (a) Find the slope of the curve y=x²-5x-4 at the point P(3.10) by finding the limit of the secant…

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Q: 5. Is the given function continuous at x=3 ? Justify your answer. Also decide, Is the function…

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Q: 5) Find the distances by drawing the figures and right triangle used to calculate: a. Between 1₁ =…

A: Given: 5. a) lines l1=2+2t, -1+t, -3t and l2=4, -5-3t, 1+4t b) Planes -x+y+2z=0 and -x+4y+2z=-6 c)…

Q: Q1: The area of the surface generated by rotating the line segment joining the points (3,1) and(6,3)…

A: To find integration:

Q: Find the arc length of x=r cost, y=rsint 0≤t≤2T

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Q: Starting from the point (2, 3, -4), reparametrize the curve r(t) = (2 + 2t, 3 + 1t, −4 + 1t) in…

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Q: Given that 2 A= 1 Lo O 0 1 O O

A: Given,

Q: Sketch the graph of the given piecewise-defined function. Identify its domain and range.          {…

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Q: Given: 4xdx + ydy + xy²dx + x²ydy = 0, Find C if x = 1, y = 1

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Q: x+y yeydy = dx

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Q: Differentiate 2ax-bxy²-cx-e²x + asinx - bcosy are constants. = 5mx y +6nxy, where a, b, c, m and n

A: Solution is given below:

Q: Explain what it means to say that lim f(x) = 3 and X 6 X→ 6+ O As x approaches 6, f(x) approaches 5,…

A: Given that limx→6-fx=3 and limx→6+fx=5

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 9-x² lim x3 3x² + x³ 3

A: Please refer to the image below

Q: Find all functions g: R → R such that (fg)' = f'g', or show that there are no such functions.

A: Given: f : ℝ→ℝ, fx=e2x3+7x and g : ℝ→ℝ such that fg'=f'g'. To find: We have to find all such…

Q: Starting from the point (−1, −1, –—4) reparametrize the curve r (t) = (−1 − 2t)i + (−1 − 2t)j + (−4…

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Q: Population Growth A major corporation is building a 4,325 acre complex of homes, offices, stores,…

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Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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Q: (x² + y² + 1)dx + x(x - 2y)dy = 0

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Q: Use the graph of the given function f to determine lim f(x) at the indicated value of a, if it…

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Q: Let f(x) be the piecewise function -2x + k f(x) = { x² + 1 if x < 1 if x ≥ 1

A: for continuous function

Q: 2. The graphs of f and g are given. Use them to evaluate each limit, if it exists. If the limit does…

A: see below the answer and explanation  as per Bertleby I have to solve first three subparts. For…

Q: F(t) = sec √² + 1 -1

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Q: Let f(x) = √√√√3+4x ƒ'(3) =

A: The function is given by fx = 3+4x To evaluate: The value of f'3.

Q: Find the indicated limit. lim (2t² - 5t + 1) t-8

A: We have to find the indicated limit.

Q: Find the surface area of revolution about the x-axis of y = 6 sin(6x) over the interval 0≤x≤ 96

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Q: 1. Given the following continuous-time signal: x(t) = t 0≤1≤1 carefully plot the following signals:…

A: Note: Since you have posted a question with multiple subparts. We will solve the first three…

Q: elimination of arbitrary constant cx^2 + y^2 = 6

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Q: See the attached image/graph and answer the following questions: (show all work) 1. What is the…

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Q: Set up an integral for the volume of the solid obtained by rotating the region bounded by the curves…

A: The given problem is solved below in detail.

Q: 1. Find dy for the following implicit function: dx cos([y(x)]² + 1) = 2x. Note: y(x) means that y is…

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Q: B)Convert r = √2 cos(0-) to cartesian.

A: Given a polar equation as r=2cosθ-π4 We have to convert given equation in cartesian.

Q: If f(x) = 24x + 10, find the slope of the secant line between the values of x1 = 3 and 2 = 2.

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Q: The limit represents the derivative of some function f at some number a. State such an f and a. 3 (1…

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Q: 1. Solve the following first order linear differential equations. Determine the largest domain for…

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Q: Given: y = 6x³, Find P.S. if y'(0) = 2 Ay (0) = 1 Oy = 3x5 + 20x + 20 O y = 3x5 + 2x + 1 O 10y = 3x5…

A: Basic identity of integration is used. ∫xn=xn+1n+1+C1

Q: Q7: The area of the region inside the circle x² + y² = 4 and above the line y = x + 2 is expressed…

A: given curvesx2+y2=4y=x+2

Q: Are the planes 2x-y-4z= 10 and x-2y+z= 4 parallel or orthogonal?

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Q: Differentiate the function. A(s) = -- A'(s) = 44 5 X

A: Given: The given function As=-11s4 To find the derivative of the function. Derivative formula:…

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A: The given bounded region is as shown below; Apply the disk method to find the volume about the…

Q: M y = e x ( ² ₁ + C ₂ x + C ₂² x ²³). c (3).

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Q: 6. Prove that curl (Vf) = 0

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Q: A = {7n +4 | neN}, B = {3n+2 | n E N}. (a) List three elements in A. (b) List three elements in B.…

A: As per our guidelines we are supposed to answer only ? 3 sub- parts ( if there are multiple sub-…

Q: 1. Find the DE of each of the following by eliminating the arbitrary constants. y = Get + C₂ cosx +…

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Q: Find the intervals on which the function is continuous.

A: NOTE: Refresh your page if you can't see any equations. .

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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Q: Solve the first-order differential equations using an appropriate method. Find a general explicit…

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Q: Find the derivative of the function f(x) = x² − 7x + 8 at the numbers (a) 2 and (b) a. SOLUTION (a)…

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