Consider the piecewise-defined function Jr+3, |1- x, x < 0, f(x) = x > 0. (a) FUNCTION, so it must pass the vertical line test! (Erase if you need to...) Graph f(x) on the coordinate plane given below. Remember f(x) is a 4 3 1 -4 -3 -2 -1 1 3 4 -1 -2 -3 -4 (b) F(0) lim f(x) =

Q: Pu 6 • (2, 5) (4, –3) Graph of f 3. The graph of ƒ is shown above for 0 < x < 4, What is (A) –1 (B)…

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Q: Find the sum of the first 21 positive integers. The sum of the first 21 positive integers is

A: We will use the concepts of A.P.

Q: Find the volume of the solid bounded by the cylinder x2 + y2 =16 and the planes y=z, x=0, z=0 in the…

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Q: Find the divergence of the vector field F. F(x, y, 2) = In(7x2+ 6y? )i + 42xyj + In(6y2. + 72² )«…

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Q: 7. If ā = -i+ 3j + k,5 = 31 – 2k and ĉ = 2î – † + 4k, determine 2(ã +5 – 2€) – (35 - 2)

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Q: A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20…

A: This question can be solved using the concept of linear programming.

Q: Find the derivative of the vector function r(t) = ta x (b+tc), where (5,-4, 1), b = {(-4, –3,1), and…

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Q: xdy + (y – cos x)dx = 0, y (- = %3D

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Q: 6. Find the indefinite integral. S 3x³ V3x4 + 7 dx (Use substitution method)

A: Solving the problem by finding the value of integration.

Q: Solve the equation algebraically. Round the result to three decimal places. 3+ln x = 0 8 e-354.598…

A: Using algebra

Q: dy If y = 3e5 . Find dz

A: Given query is to find the derivative of the expression.

Q: find Fourier series on [0,2n] 0 0<x<7 (7) f(x) =. 1 T<x<2z

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Q: 2. sin Find Maclaurin series for:

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Q: Find the e v

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Q: Evaluate r(g(t)) using the Chain Rule: r(t) = (e', e*, -6), g(t) = 5t + 6 %3| 을r(g(t)) = 《

A: Use chain rule

Q: Find V x (V × F) if F(x, y, z) = 8xyj+7xyz k. V × (V × F) =

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Q: Find the S(x* +) dx xe-1 А. 1x? + c e-1 4e xe+1 В. Ix2 + c e+1 2e xe+1 С. 1x3 + c e-1 Зе xe+1 1 D.…

A: Given query is to find the derivative of the expression.

Q: Find the conservative vector field for the potential function by finding its gradient. 9 (r,y, 2) =…

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Q: 2 and common ratio Write down the first four terms of the geometric sequence with first term (Type…

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Q: a) f(x) =(5x + 3)(7x² - 2) using the product rule b) f(x) = (3x? - 5) using the chain rule c) f(x) =…

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Q: (a²- x²}3½ dx

A: see below the answer and calculation

Q: x2 dx (x+2)3 In |x + 2| + 4x+6 4x+6 (ar+2)a +C In |x + 2| – (x+2)= Option 1 Option 2 희im lx + 2 +…

A: Given problem:-

Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x? b.…

A: area under the curve

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

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Q: 3+ 12x4 – 7x +x³ a) lim 2л2 — За3 + х — 424 3x3 +x – 4x4* - -

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Q: Dest. 3. Supply Sources! 6. 3. 10 7. 20 3. 10 11 15 30 Demand 15. 17 28 Find the initial solution…

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Q: Area A = 1,427 Calculate the definite integral f(x) dx by referring to the Area B = 2,460 Area C =…

A: Here we will find the definite integral,

Q: 5x2+11x+2 dx x(x+1)²

A: integration using partial fraction

Q: y 3.0아 (1, e) 2.5 2.0아 y-e* 1.5 1.0 y = xe*2 0.5 -1.0 -0.5 0.5 1.0 1.5 2.0

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Q: The marginal cost for a company to produce q items is given by MC(q) = 0.002q -0.7q +620. The…

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Q: If 1 f(x) 1 .3 + 1 + x 4 X° + 3 then find f'(0) +

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Q: Find the derivative of this function

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Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

A: We can solve part in the following steps.

Q: Approximate the point of intersection of the graphs of fand g. Then solve the equation f(x)=g(x)…

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Q: 2. True or False? a) -2(3BA)and 6AB'are equal vectors. Justify your answer. b) If |AB| = |AC|, then…

A: This question can be solved using the concept of equal vectors.

Q: A particle moves vertically (in inches) along the yaxis according to the position equation s(t) =° –…

A: We have to find value of t

Q: Investigate the convergence of the following series. H.' 2n+5n 2) ΣΗ-1 ILJ! 3n

A: Here, the given series is: ∑n=1∞2n+5n3n Let, an=2n+5n3n; n≥1

Q: Solve the equation for x and y x+v=300 5x+8y=2100

A: Given query is to find the solution of the system of equations

Q: AX = B is a matrixial representation of a lineal system of equations. Over the augmented matrix (…

A: Here we have to choose the correct option.

Q: Find the general solution of the differential equation. dy = xy + 3x dx

A: To find the general solution of the following differential equation.dydx=xy+3x

Q: (a) Find the directional derivative of the function f(x, y) = 4.xy – x2 – y? in the direction of…

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Q: Describe the graph of the equation. r= 5 cos t i - 18 sin 1 j +k O An ellipse in the planex = 1,…

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Q: 8. Relationship Between Continuity and Differentiability: (a) Justification needed): If lim…

A: To discuss the  relationship between continuity and differentiability.

Q: i(x) = 2-0.8(x-43.79)

A: Given query is to find the derivative of the expression.

Q: The sixth term of a geometric sequence is 1215 and the third term is 45. Find the first term and the…

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Q: Find div F and curl F if F(x, y, z) = 6e#Y i – 7 cos yj+ 9 sin² z k. div F= curl F=

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Q: Consider f(x) = 6.9x3 + 9.1x2 - 4x + 7.7. Using the given function, approximate f(4) by making use…

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Q: Consider the function f(x) = 1/3x3 + 3/2x2 - 4x. At which point(s) is the slope of the tangent line…

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Q: Use a change of variables (Substitution Method) to evaluate the following definite integral. Show…

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Q: For a plane curve r(t) = (x(t), y(t)), |æ'(t)y" (t) – x"(t)y' (t)| (x'(t)² + y' (t)²)³/2 - k(t) Use…

A: Here we have to use this equation to compute the curvature at the given point.