Find the derivative of the following function using the formula. f(x + h) – f(x) lim h-0 h f(x) = 3x² – 10x + 6 f(x) = 5x – 7

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4)

A: To find the gradient of the function at the given point.

Q: Solve th D.E using Exact -(3x² – 6.xy)dx +(-3xr' – 2y)dy = 0

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Q: Identify the open intervals on which the function is increasing or decreasing. (Enter your answers…

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Q: The marginal cost for a company to produce q items is given by MC(q) = 0.003q - 0.5q + 620. The…

A: Given: Marginal cost for a company to produce q items: MC(q) = 0.003q2 - 0.5q + 620 Company's cost =…

Q: Solve th D.E using Exact (6x² – y +3)dx+(3y – x – 2)dy

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Q: Find the gradient of the function at the given point. g(x, y) = 3xe/x, (10, 0) Vg(10, 0) = 3i + 3i

A: g(x, y)= 3 x eyx∇g(x, y) =∂g∂x, ∂g∂y∂g∂x=3eyx+3x eyx-yx2      =3eyx 1-yx∂g∂x=3eyx (x-yx)∂g∂y=3x1x…

Q: Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f…

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Q: Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f…

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Q: Suppose y(t) = 4e-5t is a solution of the initial value problem y' + ky = 0, y(0) = yo. What are the…

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Q: 3. (2x + 2)dx 1

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Q: For the function f(x,y,z) = sin -(7xyz), find f, fy, and f,. (Type an exact answer, using radicals…

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Q: Use the Comparison Test to determine whether the series is convergent or divergent. L n4/5 n- 2 1…

A: P-Test: The series ∑n=1∞1np converges iff p>1 and diverges iff p≤1 Comparison Test: Let ∑n=1∞un ,…

Q: dy (t2 – 26t + 120) = y dt

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Q: Match the indicated conditions with one of the graphs (A)-(D) shown below. 13. f'(x) >0 and f'"(x) >…

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Q: 1. y=e

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Q: in lim n' In n→∞ n!

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Q: Evaluate the indefinite integral as a power series. What is the radius of convergence? d.x 1+ x5 13.

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Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: Show that the signum function is discontinuous at x = 0

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Q: Use the Comparison Test to determine whether the series is convergent or divergent. Op Fur E n4/5 1…

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Q: Evaluate the integral. 3. [(ax-2-4) dx 2.

A: The given integral,        ∫234x-2-4dx

Q: The average student enrolled in the 20-week Court Reporting I course at the American Institute of…

A: Given function tells us the rate of change in the number of words per minute.

Q: Solve D.E using bernouliis equation r'y-x'. dy x'y-x' . dx = y* · cos(x)

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Q: Use the Quadratic Formula to solve the quadratic equation. (Enter your answers as a comma-separated…

A: Given the quadratic equation is 32x2 - 6x + 9 = 0

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Using Laplace transforms. Solve y" + 4y′ + 3y = e^t. When, y(0) = 0 and y′(0) = 0. Whole Solution

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Q: Evaluate the integral of the volume of the solid formed by revolving the region bounded by x² + y =…

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Q: e xp: (1+ e=)² 0.

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Q: For the function below, find a) the critical numbers; b) the open intervals where the function is…

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Q: the integrand of the definite integral is a difference of two functions. Sketch the graph of each…

A: Given that the integrand of the definite integral is a difference of two functions. Here we have to…

Q: Write the following expression in the form ax" + bx", where a and b are real numbers and p and q are…

A: We have to find value of given expression in the form of axp+bxq

Q: Q-5: [5 marks] Find the points at which f(x) = (x – 2)*(x + 1)³ has relative extrema.

A: Solving extreme

Q: Find all the second order partial derivatives of g(x,y) = x°y +3 sin (y) + 3y cos (x). дудх дхду

A: Use partial derivative for finding the values

Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

A: Given problem:- You are driving a car away from home. Your velocity (miles per hour) t hours after…

Q: 3) "s) Determine the highest real root of f(x) = 3x' +11,8x -17,8x-6 a) Graphically,

A: f(x)=3x3+11.8x2-17.8x-6from below graph, highest real root is x= 1.386

Q: fined ely elx ex ex + e y.

A: y=ex-e-xex+e-xDifferentiate w.r.t x

Q: Consider the curve given by the following: r = 4 cos (0),0 < 0 < n . Find the values of 0 such that:…

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Q: x – sin 2x -dx x + cos2x

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Q: Consider the following x = 2 + t², y = t² + t³. Find the following in terms of t: 1) and enter it…

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Q: Prove by Mathematical Induction. n(n + 1)(2n + 1) k² 6 k=1

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Q: WRITE THE SUMS WITHOUT SIGMA NOTATION. THEN EVALUATE THEM. > (-1)* cos kn k=1

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Q: Simplify the rational expression by using long division or synthetic division. x3 + x2 – 64x – 64 x…

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Q: A certain vehicle can accelerate from a standing start to a speed of  v(t) = −0.21t2 + 16t  feet per…

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Q: Use residues to establish the following trigonometric integral formula: »2n cos?(30) de = J,…

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Q: Determine whether the following series is converged or diverged by using the relevant test:…

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Q: A particle moves along the x-axis such that at any time t20 its position is a (t), its velocity is v…

A: Find your answer below

Q: (5) Consider the several variable function f(x, y, z) = xe²y + yeš + ze¬². Give a general formula…

A: The given function,   fx,y,z=xe2y+ye3z+ze-x

Q: In the year 2000, the population of a small city was 48,000. The population grows at a rate of r(t)…

A: Follow the procedure given below.

Q: f (x) = 1/Va; [1,9]

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Q: Consider the function below. (x) = -2x² + 4x + 5 (a) Find the critical numbers of f. (Enter your…

A: Given: For (a), f'(x)=-2x2+4x+5' =-4x+4 So, the critical number is f'(x)=0⇒-4x+4=0⇒x=1. Graph: For…