Use the gradient to find the directional derivative of the function at P in the direction of v. g(a, y) = a2 +y? + 1, P(1,2), v = (2, 3) %3D 10 V13 O 16 16 V13

Q: Approximate the root of f(x) = x - 3 with the bisection method starting with the interval [1, 2].…

A: According to Bartleby's guidelines we are allowed to solve only 1 question at a time. Apologies for…

Q: f(x + Ax) - f(x) Find lim Ax-0 Ax f(x) = 3x- 9x %3D Step 1 Find f(x + Ax) by substituting x + Ax in…

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Q: If C is the line segment from (1, 5) to, (0,0), find the value of the line integral: So(4y? i + 4x…

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Q: Find the dimensions of a rectangle with area 216 m2 whose perimeter is as small as possible. (If…

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Q: Jse the cylindrical shell method to calculate the volume of the solid Formed by rotating the graph…

A: Please refer to the image below

Q: Directions: In implicit differentiation, we differentiate each side of an equatiom wariables…

A: Topic:- function and it's Derivatives

Q: 2. Find the equation of tangent line and normal line to 3x y3 + 2y =1 at (0.2) (15 points)

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Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

A: topic - application of derivatives

Q: f(x) = sin° (tan(5e2*))

A: We can find the derivative as below using chain rule.

Q: Recall: v = can be written as v = ai + bj + ck , where i = , j = and j: . Let v = – 2i + 5j – 4k…

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Q: Determine if the given function is on the given interval Continuous

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Q: a) Find the degree 3 Taylor polynomial T3(x) for the function f (x) 4 ln(x) centered at the point a…

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Q: Using Integration by parts, evaluate: ſ xVx + 1dx Your answer

A: As per our guidelines we are supposed to answer one question, kindly repost the remaining question…

Q: 4,0 F1 Let h(x) = f(x) g(x). Find A. h'(1) В. h' (2) с. h (3) — %3D ||

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Q: Find a positive number such that the sum of the number and its reciprocal is as small as possible

A: Second Derivative Test :   Firstly find critical point of f(x).i.e, f'(x)=0 and find the value of…

Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y y= fix) 6.…

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Q: a2f_ If f(x, y) = xe?y + 6xy, then is given by: dydx O 2xe?y + 6 None of these e2y + 6 2 xe?y + 6 2…

A: We have to find the derivative

Q: given point 1. y = 2x° - 3x² - 2x + 5 ; where x 1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Let S denote the cone x? + 4y? = z². (a) Find an equation for the plane tangent to S at the point…

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Q: If A = [1 2 3], which type of the given matrix A ?

A: Given Matrix A=[1  2  3 ]1×3  Here number of row=1  Number of columns=3

Q: Differentiate implicitly to find dy/ dx. Then find the slope of the curve at the given point. x²y? =…

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Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given that  required plane passes through point ( 7, 6 , 6 )  and perpendicular to the vector having…

Q: Find the absolute extrema of the function. h(x) = ex2 − 9 on [−3, 3] absolute maximum value: ___ at…

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Q: Find the equation of the tangent line and the normal line of the curves at given point 1. y = x V16…

A: Equation of tangent line Consider y=x16+x2slope of the tangent line is dydx  at…

Q: (8x? + 2x) dx = 2x + x? Select one: OTrue O False

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Q: Solve for t. log 6 t= 2

A: Given query is to find the value of t.

Q: Using Integration by parts, evaluate: ſ x³Vx³ + 1dx Your answer

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Q: Find the gradient of the function at the given point. In(x2 - у) - 3, (2, э) Vz(2, 3) = %3D

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Q: 10. csc?e cot e1-5 cot 6 de ſ csc

A: Let's find.

Q: Use the cylindrical shell method to calculate the approximate volume of the solid formed by rotating…

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Q: J(1 - 4x4 +x)/x dx = 1/(2x) + 2x2 -x +C Select one: O True O False |(4csc?x-3sec2x) dx =…

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Q: Differentiate. f(x) = - 2 e -X t'(x) = ]

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Q: dx Assume that x=x(t) and y = y(t). Let y = x +1 and 4 when x 5. dt dy Find when x = 5. dt dy…

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Q: Consider the function Z = 2x²(1 – e-) where x and y are given to be 5 and In 5 respectively. Find…

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Q: A student throws a ball upward from a height of 48 feet, initially at 32 ft/sec. The function that…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 8. Below is the graph of Se)%3Dx+x-5x+3: a) Find the zeros. b) For each zero use synthetic division…

A: Topic:- calculus

Q: Suppose that fand g are continuous and that f (x) dr = - 2 and g (x) dr=8 Find | [5f (x) +8 (x) ]dr…

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Q: Find the general form of f if f'(x)= 9f(x). f(x) = ]

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Q: dx the correct solution of this integral is:- 1+x A) 2 V5 В) Зл

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Q: dy = (Type an integer or a simplified fraction.)

A: Topic:- double integration

Q: Find Ay and f'(x)Ax for y = f(x) = 6x, x =4, and Ax = 0.06.

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Q: In(&x³) f(x) = 1-9e-* -2x 1-9e 2

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Q: 13n Illustrate and find the smallest positive coterminal angle of 3.

A: We have to find smallest positive coterminal angle of -13π/3. And we have to illustrate that angle…

Q: S cor* (***) csc (*) da 3x+1) 3 3x+1

A: Solution…

Q: Consider the following problem: A box with an open top is to be constructed from a square piece of…

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Q: PARTA AL FRALT 1ON INTEERALS 2)

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Q: 7x - 5. Consider the function f(x) = 7x0 + 8x Enter the antiderivative of f(r) + C

A: Given the function  f(x) = 7x10 + 8x7 - 7x2 - 5. We have to find the antiderivative of f(x).

Q: Graph the equation below. Choose the correct graph. y = 5.5* OA. O B. OC. OD.

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Q: Write an equivalent exponential equation. 2 log 8 4= 3 The equivalent exponential equation is (Type…

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