Q: -Consider the function defined by the base: Find dz ) Prove that дz +y əx дz ду = sin 2z z =…
A: Topic:- application of derivatives
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Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…
A: fx and gxare integrable on the closed interval a,b and k is the constant. we have to find the false…
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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…
A: Follow the procedure given below.
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A: Concept: The acceleration is given by the derivative of the velocity That is a(t)=dv(t)dt Thus…
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A: Consider the curve Ct: rt =cost,sint,t (i) unit tangent vector The unit tangent…
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A: Follow the procedure given below.
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A: As per our answering guidelines we are allowed to solve only one question kindly repost others.…
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Q: Given the initial condition y(0) = 1, find the particular solution of the equation yy' - 6x = 0
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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s. f(t) = et cosh(t) L{f(t)}…
A: Note: Since the student has not given Theorem 7.1.1 to find the Laplace transform, so we solving…
Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…
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Q: Rewrite the following equation with the variables separated: y dy cos y dy dx = dy cos y o dy = 1 =…
A: We have to find out solutions
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Q: If [ ½ dx = 1⁄2x + 3, which of the following statements is true? / / / / dx # 1/1/2x + 3 0 / dx = x…
A: We can answer the question as below.
Q: Prove that if A and B are sets, then A - B = An BC.
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Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…
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Q: Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f(t)} and n = 1, 2, 3, . . .…
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Q: 2-₁ {2+-+5} 25. Evaluate L-1 (a) et+e-3t U (b) 2e-t+11e-3t (c) 2e- +11te-3t (d) e-t+11te-3t
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Q: The graph shown below is f (x) = √√9 - x². If g(x) = f* f(t) dt, what is g′ (√5)? g' 00 02 O 2.5 5+…
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Q: Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in…
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Q: D. Multiple Choice 1. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)],…
A: According to guidelines I can solve only first three subparts rest can be reposted.
Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…
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Q: Q10. Evaluate the following Integrals. b) /V+³ de sin (1/2) C) de
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Q: Find the derivative of G(x) = √ x³ t.csct dt. O-3x5 csc r³ cot x³ -3x² csc x³ cot x³ Ox³ csc x³…
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Q: Which of the following formulas would be used to calculate the trapezoid approximation of 0.2 3 0 T₁…
A: Here we using trapezoidal rule.
Q: Rewrite the integral using substitution: ₁x² cos(x³) dx 125 (cos u) du 25 ²5 (cos u) du 125 (cosu)…
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Q: 6 5 4 3 2- - 1 1 1 0 1 y = f(x) lim I-1 lim 2 h→0 T 3 4 5 6 7 8 Enter each answer as a whole number…
A: (i) limX→2+ fx-5fx+4 = limx→2fx-5limx→2fx+4 = limx→2fx-limx→25limx→2fx+4…
Q: . Find the y-coordinate of the centroid of the region bounded by y=x^2, y = 0, and x = 1. a. 2/3 b.…
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Q: Consider the vector-field F = (2 — ysinr − 1) + (cos x − y ). – - (a) Show that this vector-field is…
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Q: Find the derivative of the function. g(x) = [2 + (x² + 1)41³ g'(x) = 2 + (x8+ 4x6 + 6x² + 4x²+3)3
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Q: If the number of sales is inversely proportional to the price of a product, write the differential…
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A: Given the rate of change in the number of barrels, B ia proportional to 2,300,000 - B(t) Here 't' is…
Q: dx √e²x -9 A. 3 sec¹e* +C S B. 1 sec ¹ (= ² + c = c.₁ /sec²¹ e ² + C C. ex 0-¹ (+ ²) + C et с 3 D.…
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Q: Use the alternative form of the derivative to find the derivative at x = c (If it exists). (If the…
A: Given hx=x+8, c=-8
Q: S² (4-x²)³2x² dx
A: I am attaching image so that you understand each and every step.
Q: Find the magnitude and direction angle (to the nearest tenth) for each vector. C the measure of the…
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Q: mine the area of the given region. y = x + sin x 4 X 4 A 3 2- +
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Q: Please answer completely. Step by step. Evaluate. 2 [² (4-x²)³/2x² dx
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Q: dy dx What is y(2)? Suppose = 6x² + 2x − 3 and y(0) = 4. - oy(2) = 14 oy(2) = 16 oy(2) = 18 oy(2) =…
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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.)…
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Q: a) [² -da rlnr b) √ JI dr √1-² arcsin x c) / 1+ Leide [" 1+424
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Q: A tank initially contains 10 kg of salt in 50 liters of water. Pure water enters at a rate of 2…
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Q: 8) Solve the differential equation by using integrating factors. xy' = 6y + x2 y(x) =
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Q: Find the equation of the line that is tangent to the graph f(x)= 3x^3-x and perpendicular to the…
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Q: sin²0 + tan²0 + cos²0 Otan ²0 cos ³0 sin 0 sec²0 ty the e
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- Earlier in this section, we showed that we could use Fubini’s theorem to evaluate the integral ∬R x2y dA and we showed that ∫52∫31 x2y dxdy = 91. Now evaluate the double integral by evaluating the iterated integral ∫31∫52x2y dydx.Bonus: Evaluate the integral ∫ cos2 x dxEvaluate the definite integral of the following: a. ∫0π/2 cos(2x/3) dx Read as: The integral of cos(2x/3) dx from 0 to π/2 b. ∫0π/2 esinx cosx dx Read as: The integral of e to the power of sinx and cos x dx from 0 to π/2
- Write and simplify, but do not evaluate, an integral with respect to x that gives the length of the following curves on the given interval. y = x3 + 2 on 3-2, 54[Hint for (d): The resulting integral may be “easier cases” of R secm x tann x dx. More- over, it’s clear that (d) can be solved by a simple U-sub; but let’s do it now by Trig-sub as practice.]4.1 Given ∫(−2x6+3x5−3x3−6)dx, evaluate the indefinite integral. Do not include +C in your answer.