Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x)=x² +7x-7

Q: Find the solution y(t): dy dt 3. =y-3, y(0) = 2.

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Q: Let W(s,t)=F(u(s,t),v(s,t)) where u(1,0) = -8, us(1,0) = 7, ut(1,0) = -9 v(1,0) = -5, vs(1,0) = -7,…

A: Partially differentiate w with respect to s and t by chain rule of differentiation, we have…

Q: Let ECR. Show that E is Lebesgue measurable if and only if there exists a sequence of open sets…

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Q: Find the coefficient of x3y2z3w in the expansion of(2x + 3y − 4z + w)9.

A: The given expansion is 2x+3y-4z+w9. We have to find the coefficient of x3y2z3w.

Q: Determine the types of the following equations. their general solutions And find zy 4 y²dxx +2…

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Q: ey = 8 sin(x) at the point (₁4).

A: Solution

Q: What is the order of the (entire) symmetry group in R3of a 3-prism?

A: A 3-prism is a polyhedron with two congruent and parallel faces (called the bases) and rectangular…

Q: Two competing firms must simultaneously determine howmuch of a product to produce. The total profit…

A: To solve this constant-sum game, we can use the concept of payoff matrices. The payoff matrix shows…

Q: Let S = Ï an be an infinite series such that Sy = 2 - 2. n=1 N² 10 16 (a) What are the values of E…

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Q: CONVERT THE FOLLOWING 1. 2. 3. 4. 5. 6. 4/1 4 rotation → deg 3.45 rotation → deg, min, sec 3πt 5…

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Q: The annual profits for a company are given in the following table, where x represents the number of…

A: Given, Years since 2004 (x) Profits (y)(in thousands of dollars) 0 110 1 137 2 135 3 141…

Q: let (R₂ *) be a mathematical system * is defined as: FabER where axb=atbab prove that: □ is…

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

A: The given integration is I=∫0∞e-ydy We have to check whether the given integration is convergent or…

Q: X Suppose f(x) is defined for all real numbers and has continuous derivatives of all orders for all…

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Q: Complete the description of the piecewise function graphed below. Use interval notation to indicate…

A: We have to complete the description of the piecewise function graphed given.

Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

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Q: Problem 3. Let X = {(0, 0), (2, 0), (0, 2), (2, 2)}. Give an explicit expression for Rips(X, r) for…

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Q: Find the measure of the indicated triangle n=7y° O=(4y-15)° m=?

A: we know that any triangle have three angles and sum of this three angles is 180°

Q: Let A = 3 2 and b = 2 -5 7√2 6 1 3 2 = 7 7√2 28 3 7√2 14 [7 8 2022] The QR factorization of the…

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Q: Suppose that f: R → R is a continuous function. Show that there exists a point on the graph of f…

A: Given: f:ℝ→ℝ is a continuous function. We need to prove that there exists a point on the graph of f…

Q: QUESTION 4. Draw qualitative phase line diagrams for the differential equation y' = 2y³ - y² + ay,…

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Q: 36. Area of a Polygon Green's Theorem leads to a convenient formula for the area of a polygon. (a)…

A: Given: C be the line segment joining x1 , y1 to x2 , y2. To Show : a) Area of a polygon with the…

Q: (7) Let F(x, y, z)= y cos(ry) i+r cos(ry) j-sin(z) k. (a) Find curl F. (b) Is the field F…

A: Given,           F→(x,y,z) = ycos(xy) i→+ xcos(xy) j→- sinz k→ Let,    M= ycos(xy),     N= xcos(xy),…

Q: The Determinant of a Scalar Multiple of a Matrix In Exercises 7-14, use the fact that |cA| = c"|A|…

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Q: If limf (x) = 62 and f'(x) is positive for all x, what is lim f'(x)? (Assume that this limit…

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Q: Q1. Control charts for X and R are maintained on a process. After 20 preliminary subgroups each of…

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Q: Let y = proj₁y = 3 -2 and u = -3 (a) Find the orthogonal projection of y onto u. 2 1 = (b) Compute…

A: Here we have to find orthogonal projection of y onto u and also we have to calculate distance d.

Q: Let V be the two-dimensional subspace of R4 spanned by (0, 1, 0, 1) and (0, 2, 0, 0). Write the…

A: To find v, we need to find the projection of u onto the subspace V, which can be found using the…

Q: 2. a) b) Let V R³. Let W be a subset of V where W = The vectors = {(20 + 30 ) ER ₁ USER} b a, b 2a…

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Q: Find the inverse, if it exists, for the given matrix. 1 -1 2 1 -1 2-3 4 0 Select the correct choice…

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Q: Solve the given system of differential equations by systematic elimination. day=9x-e² (x(e), (e))-(…

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Q: 2 If the time. =1 moves in Such wery 1-12 + ²√2 = 1/², where c is a constmit, then 92 b Prove that…

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Q: Complex Numbers Evaluate A= sin(0.573+j0.783)²

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Q: Let H= X { ;] 182² +47²=1}\x 5x² y which represents the set of points on and inside an ellipse in…

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Q: Show that that if 5 divides 2x + 1, then 25 divides 14x 2 + 19x – 19 is true for all positive…

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Q: Prove that for any finite X C R¹, Rips(X, r) C Čech(X, 2r).

A: To prove that for any finite X⊂ℝn, Rips(X,r)⊆check{C}(X,2r), we need to show that any simplex in the…

Q: If the radical axis of the circles x² + y² + 2gx + 2 fy+c= 0 and 2x² + 2y² + 3x +8₂ touches the…

A: Given: Here the radical axis of the circles given x2+y2+2gx+2fy+c=02x2+2y2+3x+8y+2c=0 we have to…

Q: In Exercises 5 and 6, compute the product AB in two ways: (a) by the definition, where Ab₁ and Abê…

A: The given matrices A=-12542-3 and B=3-4-21. We have to find the matrix AB by using the given two…

Q: Yummy Yogurt sells yogurt at three locations. Location I sells 47 gal of nonfat, 40 gal of regular,…

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Q: Let A be a non-singular matrix over GF(2). Consider the affine transformation f(b) = A b + c, where…

A: Given: A is a non-singular matrix and fb=Ab+c is an affine transformation.To find: Inverse…

Q: 3. Determine the truth value of each of the following quantified statements. If a universally…

A: Since you have posted a multi subparts question according to guildlines I will solve first(j,k,l)…

Q: Show that the following graphs are not isomorphic: #

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Q: Let M be the group of all real 2 x 2 matrices under addition. LetN = R ⨁ R ⨁ R ⨁ R under…

A: Given: M is a group of all 2×2 matrices under addition. N=R⊕R⊕R⊕R under component-wise addition. To…

Q: Use cylindrical shells to find the volume formed by rotating the region in the first quadrant…

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Q: The position of a baseball (in ft) is represented by r(t) 40√2ti + (3 + 40√2t - 16t²)j. Find the arc…

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Q: The length of a stalactite (in mm) has been measured at the beginning of every fourth year since the…

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Q: Determine the LU decomposition of the matrix a = 24 6 3 5 1 using the Gauss elimination procedure.…

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Q: The differential equation dy - -2xy² - 2xy + (-2x²y — 1x² + 3) da Has solutions of form F(x, y) c…

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Q: 2 The equation of three circles are given x² + y² -1, x² - y² − 8x + 15 = 0, x² + y² + 10x + 24 = 0…

A: We know that the point from which the lengths of tangents are equal in length is the radical center…

Q: Assume A is a bounded, non-empty subset of R. Let r = sup(A). Prove there is a sequence from A…

A: Given r=sup(A). Let r∈A.  Consider the sequence {xn} such that xn=r ∀n∈ℕ.Then {xn} is a sequence…