Recall from calculus, if a function is differentiable at a point c, then it is continuous at c, but that the converse of this statement is not true (for example, f(x) = |x| at the point 0). Restate this fact using "necessary and sufficient" language.

Q: Determine the explicit formula for the nth term of the sequence written below. Note that the first…

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Q: 4. Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = y - y and…

A: We have to find moment of inertia about the x -axis.

Q: In standard normal distribution, what is the area between z = 0 and z = - 2.13 under the normal…

A: Given that, the range is -2.13 to 0.

Q: The functionf:R->R defined by f(x) = (x2+ 1)35 for all x e R is A. One-One but not onto O B. onto…

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Q: A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside and…

A: We have to find the area inside and concentric to the larger pentagon but outside the smaller…

Q: Find 2(A+B) ( Matrix Addition & Scalar Multiplication). 4 3 -2 -5 2 3 B = -2 -3 4 6 -1 -2 A = 6. -1…

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Q: | f(t)f(t – t)dt = 6t³

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Q: Prove that if n is a +ive integer,

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Q: ... .......s ..... ...

A: Let's take first class tickets as x, where x > 25 Coach tickets as y, where y > 40. On each…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: y" – 3y' + 2y = est ; y(0) = y'( %3D

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Q: Calculate (13, 000 +2)10 (mod 13). Find the omeir lor of 3456 whon dlivided by the following Hint:…

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Q: Find the coordinate vector [x]R of x relative to the given basis B= {b,. b2, bg}.

A: Here we have to find the coordinate vector [X]B of X relative to basis B.

Q: Show that for every n ∈ N there exists an irreducible polynomial of degree n in Q[x] (hint: use…

A: The complete solution is in given below

Q: Suppose a coin is flipped and a card is drawn from the deck. What is the probability that the coin…

A: Given that Coin and card We have to find probability

Q: Consider the following. (x, y) = x/y, P(2, 1), u=i+ (a) Find the gradient of f. V{x, y) = (b)…

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Q: b) Use the Ratio Test to determine if the series converges or diverges. n5" Z (2n + 3)ln (n + 1) n=1

A: Given series is ∑n=1∞n5n2n+3lnn+1

Q: Move the sliderk so that the graph of y = 2" gets shifted up 3 units. Then type the new function,…

A: We have to slide the k such that graph shifted 3 unit up.

Q: M{sin x; p}

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Q: How many subsets are there of the set (1, 2, 3, 4, 5, 6, 7, 8, 9, 10} which contain at least three…

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Q: 20 – 33 Use the method of Laplace transforms to solve each IVP. 20. y+10y=f, v(0) 0 T プレ 28 )- 3,…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: What is the general solution to the differential equation (2x – 2y – 3)dx = (2x – 4y – 2)dy ? 2у -…

A: Solve the first order linear differential equation

Q: (a) If b² – 4ac = 0 and y1 = em# solves ay" + by/ + cy = 0, use reduction of order to get a linearly…

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Q: State whether each of the following series converges absolutely, conditionally, or not at all. n…

A: Given series is ∑n=1∞(-1)n+1nn+3

Q: Find a set of parametric equations for the line passing through the point (6, 0, 7) that is parallel…

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Q: 1)z = e(4+j3) In(6230") 2) z = (-;)(* 2) z = (-)(r)"

A: (1) The  given complex equation is                                                Z=e4+j3ln6∠30°

Q: If csc e = 1/3t, then where defined, cos 0 A) Square root of (1 – 9t²) 3t/squareroot of (1 – 9t2)…

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Q: Prove that TIN) F(a – p) O< Re

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Q: Given z= -5 - 8i, what is z in Polar form?.

A: The polar form of a complex number a+bi is reiθ, where r=a2+b2, tanθ=ba. Calculate the modulus of…

Q: Mellin transform

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Q: Use a calculator or program to compute the first 10 iterations of Newton's method when they are…

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Q: Evaluate: sin(0) – cos(0) dO

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Q: M [xP (1 – x)<-1 2F1 (a, b; c; 1- x) H(1 – x); p] = T (p - a + c + p)r (p – b + c + p)

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Q: In Exercises 5–8, let S be the collection of vectors y in R' that satisfy the given property. In…

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Q: Find the area to the

A: Given, the left of z=-1.96 or to the right of z =1.96.

Q: 4. {3k}

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Q: Jompute the line integral | (yzev +y? + z - 2r) dr + (rze"ys + 2ry) dy + (rye*v= +x +32?) dz, where…

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Q: Given D = 6p sin ø a, +1.5p cos o as C/m², evaluate both a) S,D'dš p=2,o<¢<T,0<Z<5 6) p:…

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Q: Find the minimum value of f(x1, X2) = 2x, + 3x2 subject to the following constraints. Write the…

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Q: 100 7. dx

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Q: Find a linearly independent set of vectors that spans the same subspace of R' as that spanned by the…

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Q: ne eigen-spaces correspondia

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Q: (a) . Let x E Z. List all possible remainders of 7x² when divided by 3. Justify your answer. (b) [ ]…

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Q: horizontal or vertical

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Q: MATH Make a two-column proof to show that the triangles formed by the diagonal of the Futsal court…

A: Draw a rectangle ABCD and join the points A and C. Note: Opposite sides of a rectangle are equal.…

Q: Compute the first derivative of y = 2x^4 - 6x^3 - 12x - 8 at the point x=0 based on the value at xo…

A: Five point FD Approximation and CD Approximation:--- ..  I this Error is 0%

Q: cos(s")dtds

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Prove Corollary 6.2. If L: V → W is a linear transformation of a vector space V into a vector space…

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Q: If T : R³ → R³ is a linear transformation such that (E)-E (E) (E) T T 3 then T

A: Given that T:ℝ3→ℝ3 is a linear transformation such that T100=321, T010=-4-2-3 and T001=334 We have…

Q: a + bx? dx 3ax + bx

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