Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0 The instantaneous rate of change at x = 0 is

Q: Find the derivative of the function. - 5x - 4 e to y=xe dy dx ||

A: Finding the derivative of the function

Q: If A = 3ai +4j-k and B=4i+j-3k, find the value of a if A normal to B.

A: Given A→=3ai^+4j^-k^  and B→=4i^+j^-3k^

Q: {CLO-3} Find the absolute minimum value of the function f(x)=x²-3x²-24x +5 on the closed interval […

A: This question can be solved using the concept of absolute maximum and minimum.

Q: Can you elaborate you answer in b>? I cdont understand whiy it became 4

A: We have to elaborate why the angle is 4π3.

Q: Find all the local maxima, local minima, and saddle points of the function. 3 f(x,y) = x³ +y³ + 3x²…

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Q: 3 Só ( x + ²/2 ) ²³ dx X

A: integration

Q: Find at least 5 distinct rational points on the unit circle in the first quadrant of the plane.

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Q: Find the point on the plane 5x + 4y + z = 11 that is nearest the origin. What are the values of x,…

A: First we find the distance(d) between a point (x,y,z) on the plane and the origin .Then form a…

Q: Complete the following. (a) The graph of y = g(x) is shown. Draw the graph of y = g(-x)+1. ? -8 -6 A…

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Q: Əw Given w = xysin(z²), x=s-t, y=s², z t². Find Əy əw ду = y sin z ² Option 1 O Option 3 aw = x sin…

A: Topic:- derivatives

Q: Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y =…

A: Let's find definite integral of arc of length of given parabola y =4-x^2.

Q: 1. If F(x) = ∙e S ex е et² dt, find F(1) and F'(x).

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Q: The equation of the tangent line to the graph of f(x)=ln|x at x = -2 is v=²(x+2)+n2 (a) TRUE (b)…

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Q: Consider the following double integral 1= dy dx. By reversing the order of integration of I, we…

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Q: Find the point (if it exists) at which the following plane and line intersect. -2x-10y-10z = -19 and…

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Q: 2. If x = 2a-3b-4c, ỷ = −2ã + 3b + 3c, and ž = 2ã − 3b-5c, determine the simplified expression for…

A: vector

Q: Find the particular solution (D² + 4D + 4)y=0 when x = 0, y = 1 and y = -1 What is the particular…

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Q: S 10dz 4z³-4z² + 5z

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Q: Given the following set of data X 1 1.5 1.6 2.5 3.5 f(x) 0.6767 0.3734 0.3261 0.08422 0.01596 Find…

A: Solution of the problem as follows

Q: If f is a differentiable function and f'(x)=x55x4+ 5x³+2, then f is concave up on

A: As per our company guidelines we are supposed to answer only one question. Kindly send other…

Q: Find the gradient of f(x,y,z) = (x² + y² + z²) 23 26 Vf|(-2,2,-1) = i+ 23 54 |j+ 54 27 (Type…

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Q: 7. The particular solution of (D³ + 2 D²-5D-6)y = 0, when x = 0, y = 0, y = 0, y" = 1

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Q: 2) For hyperbola, consider the following graphs * *(

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Q: 6. Sketch the vector w on the grid on the right and label its coordinates. Vectors and + w are…

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Q: 9-11. Solve the derivative using chain rule. y = x + 8x² + 16.

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Q: Evaluate the following integrals: O •(Cartesian to Polar) Civen the cartesian coordinate find FOUR…

A: Follow the procedure given below.

Q: Əw at = xysin(z2), x= s-t, y=s2, z t². Use the Chain Rule to find .

A: We know that derivatives of d(xn)/dx = nxn-1. And d(sinx)/dx = cosx  Here i attached the solution of…

Q: -1 position (s, cm) 153 10- 5+ 0 2 3 4 time (t, seconds) 5

A: Slope of position(s) graph gives speed. i.e. Speed =dsdt

Q: Find the point (if it exists) at which the following plane and line intersect. - 10x-3y-9z= - 19 and…

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Q: How to solve dx = 2dy = -2dz.

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Q: 5s +4 83 None of the Choices. Option 1 5t + 2t³ 5t - 2t³ Option 2 Option 3 Option 4 2t + 5t³ 2t -…

A: Let's find inverse laplace of given  function.

Q: The following data shows the height function of a hill a a distance x from a reference. Form a cubic…

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Q: (CLO-3) Find the absolute maximum value of the function f(x)=x³-12x+3 on the closed interval [-4,3].

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Q: y = 25

A: Topic:- function

Q: Evaluate the triple integral zdV, where E is bounded by the cylinder y² + 2² = 4 and the planes z =…

A: Given problem:- Evaluate the ∫∫∫E z dV, where E is bounded by the cylinder y2+z2=4 and the planes z…

Q: Use cylindricoll shells to find the volume shells of the solid obtained by rotating the region…

A: Given region is bounded by y=x2 , y=0 and x=6 rotating about y -axis

Q: [CLO-2] Evaluate the Indefinite integral by using the substitution rule. S√tan (x) sec²(x) dx…

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Q: The region bounded by the ellipse 16x^2 + 9y^2 = 144 is revolved about the x-axis. Find the volume…

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Q: Question 2 What is the slope of the tangent line to the graph of x² - xy - 4y² + 2x + 4y = 8 at (4,…

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Q: Determine whether the following function is differentiable at x = 9 f(x)=√x²-16, x<9 √x, x ≥9 (a)…

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Q: If A = 3ai +4j-k and B = 4i+j-3k, find the value of a if A normal to B.

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Q: Find the Laplace Transform of the following functions

A: Laplace Transform of function cos3t

Q: Consider the positively oriented surface S₂ defined by the vector function R(u, v) = (u sin v-3, u…

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Q: This question is designed to be answered without a calculator. Use this graph of function f. y 5+ in…

A: Here, from the given graph the function is continuous at x=0,2,4 but not continuous at x=-2 because…

Q: Consider the following function, f(x) = x³, 3 a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate

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Q: If à = 3ai +4j-k and B = 4i+j−3k, find the value of a if A normal to B.

A: Given vectors A→=3ai+4j-k and B→=4i+j-3k

Q: Compute the general solution to the second order linear non-homogeneous differential equation: d²y…

A: Given differential equation, d²y/dx²-2dy/dx=8sin2x Corresponding homogeneous equation, (D²-2D)y=0…

Q: The critical number(s), if any, of the function f(x) = (x²-3x+2) is (are):

A: critical points of fx=x2-3x+2-13

Q: Q1): Prove that: A square matrix B has inverse if and only determinant of B is not equal zero.

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Q: 1 83 -8 14(e++e²¹) Option 1 - 1 + ½ (0²¹ + ²) Option 2 1+1(e²¹+ e²) Option 3 - -/-(e²+ + e²) 1.…

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