Find the directional derivative of f(x, y) = x² - 2xy at the point (1, -2) in the direction from P(-1,2) to Q(2,3).

Q: If f (x) = 1 and (a, ƒ(a)) and (a + h, f(a+h)) are points on f(x), where h = 0, then 2x -1 f'(a) =…

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Q: Use the properties of the derivative to find r(t) = 3/i+6f³j+31³k u(t)=2i+2r²j-3t³k [r(t) - u(t)]…

A: This question is related to derivative, we will solve it using given information.

Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 14, (1,…

A: We have to solve given Questions.

Q: The position in feet of a race car along a straight track after t seconds is given by s(t) = 4t² - t…

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Q: Fill in the blanks: x² + The equation describes an ellipse. The volume of the solid obtained by…

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Q: 18 What is the total degree G? 3 6 5 VI e₁ V2 ez VA

A: From the given graph G, we have to find its total degree

Q: Fill in the blanks: Use integration to find the volume of the solid obtained by revolving the region…

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Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = −1 and B ′(24) =…

A: Given thaty=B24 x=24y=B24 =-1B'24 =-14To :find equation of tangent line Solution :equation of line…

Q: Q1A)The vectors A = 3i+j+ 4k, B= 2i-3j-k, find vector normal to A and In plane of A and, B.…

A: Let's call the vector to be found is C. C vector will be normal to both vector and A and B. we can…

Q: 31 Matrix A =[42],find Eigen values of A².

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Q: Evaluate f(sinxcosx + tanxsec² x) dx O-[sin²x + tan² x] + C O tan²x - sin²x + C O sin²x - tan²x + C…

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Q: ди 2²u Consider the heat equation = +2x, for a bar of length L=1, with non homogeneous boundary…

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Q: Evaluate the following integral. 48x² S dx (x-15)(x+5)²

A: Solution of given question is written in below steps.

Q: t=sin³x B) [2 sintdt cos(sin 2x)sin 2x dx- A) sintdt D) [ 2 cos tdt →? c) fcos tdt E) fcos 2tdt 4.…

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Q: Use Euler's method with step size 0.1 to estimate y(0.4), where y(x) is the solution of the…

A: To solve the initial value problem.

Q: -4 -3 -2 -1 0 3 4 1 2 Write an interval to describe the set of values shown above.

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Q: Find given that x = sec² y. dy dx Osec² ytan y cos² ytan y Osin² y cot y Ocos² y cot y

A: We know that derivatives power rule is  d(xn)/dx = nxn-1.     Here i attached the solution of this…

Q: The manager of a restaurant found that the cost to produce 100 cups of coffee is $10.55, while the…

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Q: dx dt 4x + y dy x + 2y dt a) Find the general solution for x(t) and y(t) b) Solve the initial value…

A: Given that,

Q: dy Solve the differential equation dx x6 +4y X

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Q: I(X) {(-2,1), (1,4), (2,5), (3,6) g(x) = 6 + 4x h(x) = -x² + 2 2. 2h(3)+g[f(-2)] find 1. h[f(1)] 7…

A: 1. hf17=h47                  =-16+27                   =-147                    =-22.…

Q: Find area bounded by y=0,y=√x-x² using double integration.

A: To find the area of the given region.

Q: The y-intercept of the parabola y = - (x-20)^2 + 100 is

A: The given equation of the parabola is: y=-x-202+100   As we know that; To determine y-intercept, we…

Q: 1. The radioactive isotope hydrogen-3 has a half-life of 12.3 years. a. If a sample of 80 mg of…

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Q: Find the first derivative of -5x²+2x-5 210x -5x²+2x-4 ебх о о 5x2-2x+5 P5х 2 x2+1 e5x

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Q: Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient…

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Q: dz - 6² 7 4 16 + Consider the integral 7² +16 du ONI - S = (2-16) a) I= /0 du O b) I 117 So u (u -…

A: Given :I=∫01dz7z+16

Q: 11. Draw a high-quality graph by hand on graph paper for the function f(x) = 2x³ + 6x². Your work…

A: Given :  f ( x ) = 2x 3 + 6x2  find minimums , maximums and inflection points ,  And intercepts

Q: find f'(a) f(t) = 1/(t2+7)

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Q: Find the general solutions of the system. 7-9 0 x' = + 1 13 0 x 1 3 10 x(t) =

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Q: ubscription. a. Based on the graph of J, hind the root of the equation 6x³ 19x2 + 16x-4 = 0 that is…

A: We need to find root.

Q: lim x²+3x sin x x-0 0 3 01 O does not exist 0 0

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Q: Find an equation of the hyperbola that has foci at (0, -15) and (0, 15), and asymptotes y= 3 3 2x…

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Q: Which of the following interval is f(x) = O (2, +∞0) O [2, +∞0) 0 (-∞0, +∞0) ○ (0, +∞) 1 Vx…

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Q: ind area bounded by y = 0, y =√x-x² using double integration.

A: We have to find area of given region.

Q: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

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Q: At point (1,-1,2). 4

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Q: Assume that f is continuous on the set of real numbers. Find a and b given that cb 3 f(a)da - [³…

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Q: Assume that f is continuous on the set of real numbers. Find a and b given that b 3 [ f(x) dx - f₁…

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Q: Solve by Gaussian-Jordan algorithm (reducing to rref). Show all row operations you apply. If the…

A: First we reduce in row eclehon form .

Q: Əw 1. If w=x" f() show that x ax +y Əw ду = nw where n = integer.

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Q: Using the Inverse Function Theorem, what is (-1) (8) given that (x) = √6x-2? Note that (11)= 8. (Do…

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Q: The vectors A = 3i+j+4k,B=2i-3j-k, find vector normal to A and In plane of A and, B.

A: To find the Normal vector to A & B.

Q: Use logarithmic differentiation to find y = (In x) sin, x> 1. dy dx given

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Q: B)Solve differential equation dx = -(x²+y) x+siny

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Q: Use any method to evaluate the integral. dx X>11 (x²-121) 3/2

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Q: Find the unit tangent vector T(7) for the line tangent to the space curve r(t) = (12 cost, 12 sint,…

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Q: Given f(x) = 3-5x³, use a table to estimate the slope of the tangent line to f at the point P(0, 3).…

A: According to question,Given Function,fx = 3-5x3P0, 3Qx, fx

Q: The slope of the oblique asymptote to the curve f(x) = x +11 corresponds to

A: folllow the procedure given below.

Q: Assume that the random variable X is normally distributed, with mean μ = 70 and standard deviation…

A: To find the probablity P(X>a)  then we have to convert the expression into  Z-score value of the…