Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) Vf(4, 2) =

Q: endicular to the plane z + 3y – x = 7 and containing the points (2, 5, 0) and (0, 2, -1)

A: Here we have to find the equation of plane which is perpendicular to the other plane.

Q: Solve the following differential equations using the method of undetermined coefficients. y" + 4y' +…

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Q: Find the value of § cot³(x) cosec“ (x).

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Q: please asnwr

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Q: Evaluate * (1 – x²)3/2° 1 + c 3 1-x2 -1 + c /1 – x² O Option 4 Option 2 2 1 1 + c /1 – x² :+c 3 V1-…

A: ∫ xdx/(1-x2)3/2 here assume that  1-x2 = u -2x = du/dx xdx = -du/2 ∫ -du/2u3/2 ∫ -u-3/2du/2 2u-1/2/2…

Q: Solve the differential equation with the appropriate method. Finalize the answer equated to y. 1.…

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Q: Find the volume of the solid formed by revolving the region bounded by the curves x=2√y, y=0, and…

A: The graph is shown below, where the chex region represent the required volume to find.

Q: Evaluate | sin(In t) dt. t sin(In t) – t cos (In t) -t sin(In t) – t cos (In t) . . 2 2 O Option 1…

A: Substitute u=ln(t) ⟶ du/dt=1/t dt = tdu t = eu ∫ eusinudu we use integration by parts ∫fg′=fg−∫f′g f…

Q: The value of the double integral // (2x²y + 9y') d A, D where D is the region bounded by x and y = 2…

A: Given problem:-

Q: (2) use tue limit Couperisen Tert to defermine tue canleryencl or divergence of tud series Ź 3 sin…

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Q: Use the Midpoint approximation method to approximate the area under the graph of the function f(x) =…

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Q: Given the region bounded by y=×^3 ,X = 2, and the x-axis (in Quadrant I) is rotated about the line y…

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Q: y = Vx, x = 0 , y = 2 , revolved at y axis

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Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

Q: Given the graph of f'(x) below. (a) Find the intervals on which f(x) is concave up/concave down (b)…

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Q: 1. fx³e*/2dx /4 2. S*x sin 2x dx

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Q: Find the area of the parallelogram that has u = 2i – j + 2k and v = 2j + 3k as adjacent sides. NOTE:…

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Q: Use a trigonometric identity to find cos (x - 5) if sin (x) = (Express numbers in exact form. Use…

A: Given,            sinx=67To find : Find cosx-π2.

Q: Check the continuity of the function at x : = 0 and x = 1

A: Given,           The piecewise function is given below :            fx=-2; -4≤x≤-1x-1; -1≤x≤0x2;…

Q: Is) Determine the minimal number of terms requined to epproscimete fue fum of tue series with an…

A: Using the alternating series reminder theoram to find the number of terms.

Q: * sin" (3y) cos" (3y) dy 10 (3y) dy COS 15360 111546435 256 156009

A: Given:   Given:    ∫0π6sin133ycos103y dy

Q: 6. gx) VX- 3 at x = 4 三 7 g(x) at X = 8 三 e1 gCX)= n4ーメ at x =0

A: Given

Q: simplify

A: We have to simplify  of the given expression

Q: Explain why S is not a basis for R2. S= {(3, 5), (1, 0), (0, 1)} O sis linearly dependent. O does…

A: The given set S=3,5, 1,0, 0,1

Q: xD'(x) Find the demand function q = D(x), given the elasticity conditions. Recall that elasticity of…

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Q: Evaluateſ (3x + 2)dx A. 3x2 + 2x +C B. 2x² + 2x + C c 를2 + + 2x + C D. + 2x + C

A: The objective of the question is evaluate the indefinite integral and choose the correct option.

Q: Find the Fourier series of f(x) as given over one period and sketch f(x) and partial sums: so if…

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Q: it. notation and fractions where needed.)

A: We have to find the value of the given limit according to the rule of limit

Q: |. IF A FORCE OF 80 lb STRETCHES A 12t SHRink Ift. FIND THE woRk DONE IN STRETCHING IT a) PRom Izto…

A: work done = force*displacement here  a from 12ft to 15 ft  3 ft displacement  work done = 80*3 = 240…

Q: State the answer using combinations. c) The number of edges in the complete graph K21. d) How many 7…

A: We will answer only part c, d and e because you have mentioned to solve only these three.   Complete…

Q: Let u - (1, 2, 3), v (4, 4, -2), and w = (3, 0, -3). Find 4u + Sv - w. STEP 1: Multiply each vector…

A: The solution is given below

Q: Use x = au, y = bv to show that the area of the ellipse x2 y? = 1 is rab. 62 a2

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Q: 5. Use L'Hospital's rule to compute the following limits (a) lim a In(x) (b) lim sin(z) (c) lim…

A: Here are the solutions: We will use L'Hospital rule and differentiate the numerator and denominator…

Q: Let f(x)=4x^2−4x^4. Find the open intervals on which f is increasing (decreasing). Then determine…

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Q: solve the exponential equation by using the property that b^x= b^y implies x=y, for b>0 and b≠1.…

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Q: 7458 B2 Follow the solution format on the picture.

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Q: Evaluate the following integral using trigonometric substitution. хах Vx2– x – 1 а.

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Q: B) By using (A), Find lim /-

A: limn→∞1n

Q: Solve the following differential equations: (DE in 1st Order, 2nd Degree) 7.) (v')² +| x – 2x y'+x -…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the slope of the tangent line to the given curve at the point corresponding to the specified…

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Q: dx. J x² + 2x + 5 x+1 11 arctan x+1 11 ;+ 2x – In [/r² + 2x + S- *+ 2x + In Vx? + 2x +5+, arctan 2 2…

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Q: 7. The function f (x,y,z) = xyz, when subject to the constraint x + 2y + 3z = 72, has one critical…

A: 7. The function f(x, y, z) = xyz, when subject to the constraint x + 2y + 3z = 72, has one critical…

Q: 1. Logarithmic differentiation. Compute the derivative of each function using logarithmic…

A: Due to bartleby guidelines,we have to solve only 1 question so if you want another answer so please…

Q: O y" + y 0 O y" - 5y' + 4y = 0 O y" + 2y' + 2y = 0 O y" - 3y' - 4y = 0 O y" + 2y' + y = 0 O y" + 9y…

A: Curve

Q: Find the arc length in the second quadrant of the curve x23 +y2/3 = 25 from x = - 125 to x = – 8.…

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Q: Let a ci + j and b 2i + 6j. Find c so that a and b are orthogonal. C =

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Q: Use the Laplace transform to solve the given integral equation. f(t) + (t – t)f(t)dr = t 1 f(t) = s“…

A: Hi! The answer to the solution was f(t)=sint. You have entered the answer incorrectly.

Q: Find a formula for f'(x) and determine the slopef'(2) for the following function. f(x) el+8r' In(x+…

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Q: Question Is S (;x² + 5x + C)dx = 3x + 5 correct? %3D CLAIM EVIDENCE REASONING

A: ∫  3x2/2 +5x +cdx now integrate it 3x3/6 + 5x2/2 +cx +c x3/2 + 5x2/2 +cx +c this is the answer  so…

Q: Find the angle 0 between the vectors in radians and in degrees. - co) + sin() = cos 4 u = cos i +…

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