Graph the function and the indicated tangent line. Graph f(x) = -4x2 and the tangent line to the graph at the point whose x-coordinate is -2.

Q: nd the limit (if it exists). (If an answer does not exist, enter DNE.) 15 lim (x,y) → (0,0) x6y²

A: To  find the  limit.

Q: , 4x²+x+17 (x+1)(x²+4) dx I

A: Hee, to evaluate the given integral we have to rewrite the rational function.

Q: Use the given acceleration function to find the velocity vector v(t), and position vector r(t). Then…

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Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

A: Find determinant of coefficient Matrix  Then find delta x ,delta y, delta z

Q: • The orthogonal trajectory of the equation given below is already given. What is the value of "n"?…

A: The given equation x2+3y2=r2

Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) 02 dx ; u nein!! sin x+cos x (2) […

A: We have to calculate the given indefinite integral according to the given information

Q: Q1/ Solve the following differential Equations. 1- (1+x2)dy-xy dx = 0

A: To solve the differential equation.

Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1

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Q: (B): If A = 2i +3j - 4k; B = 3i-4j+5k and C=i+j-k, find: (ii) B.C (iii)A. (B+C)and (A + B).C (iv)…

A: Given: A→=2i+3j−4k;B→=3i−4j+5k and C→=i+j−k We know that x1i +y1j+z1k·x2i +y2j+z2k = x1x2+y1y2+z1z2

Q: Q2: Find the 1. y = 1- 2. y [In(x² + 2)²]³ 3. y = xcsex tan² (cos x) 4. y for the following…

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: ¡¡y y cos x² dx dy Evaluate the double integral by reversing the order Show your answer in details.

A: Change the order of integration and then  change limits respectively

Q: Solve the given initial-value problem. y(x) = y" + 6y7y = 11e2x, y(0) = 1, y'(0) = 1 2x -7.x 7e +…

A: We can solve the given initial valued problem .

Q: Given the equation 5 sin 6xy = 3, evaluate dy Assume that the equation implicitly defines y as a…

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Q: (A): Solve the following linear equations by Cramer's rule: x + y + 2z=1 2x-y-z = 0 = 4 x +2y-z

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Q: Describe the level curves of the function. z=x+y, c= -2, 0, 2, 3 O The level curves are parabolas.…

A: We need to choose correct option.

Q: Question 5 Test the series below for convergence using the Root Test. 5)₁ ∞ n=1 f(n): 3n 6n + 5 The…

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Q: 3. The radius of a sphere ball is measured at r = 25 cm. Estimate error in the volume and surface…

A: The radius of a sphere is measured at r = 25 cm. We have to estimate error in the volume and surface…

Q: Find the unit tangent vector T(t). r(t) = t²i + tj +4k, P(9, 3, 4) TO) (No Docpopcol

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Q: Find both first partial derivatives. z=(4 xy)/(x^2+y^2) fx(x,y)= fy(x,y)=

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Q: 4. [0/11.11 Points] A rectangular page is to contain 54 square inches of print. The margins on each…

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Q: g(x) dx = (Simplify your answer.) 7 4g(x)dx= 2 (Simplify your answer.) 7 [g(x)-f(x)]dx = (Simplify…

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Q: S 2 (2 x ² + 1 ) 1²/1 2 dx

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Q: (B): If A = 2i +3j - 4k; B = 3i - 4j+5k and C = i + j-k, find: (iv) (3A + 4B).C (i)A.B (ii) B.C…

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Q: For what values of a and b is the line 2x + y = b tangent to the curve y = ax² when x = 4?

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Q: Find a differential equation of the following family of curves whose solution is: 1. A family of…

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Q: (d) Determine the y-intercept(s). (e) Sketch the function. (f) Determine the axis of symmetry. (g)…

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Q: 1. Find the second-order prediction error filter and the prediction error variance for the random…

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Q: Evaluate the indefinite integral as a power series , x² ln(1 + x)

A: We want to find the indefinite integral as a power series.

Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin(A) 00 7 A

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Q: ddw? dt (C): If w = tan x and x = 4t³ + t ; Find

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Q: Many patients get concerned when a test involves injection of a radioactive material. For example…

A: Given :   The curve is to be fitted R = Ae(Bt) Taking log both side  log10(R) = log10 A + Bt log10…

Q: Given f" (x) = 8x − 6, ƒ' (1) = −3, and f(1) = 5 find f(x).

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Q: What is f'(x) given the integral function •5x+1 f(x) = 5x+¹ cos(e") du? ○ f'(x) = 5 cos (es) o f'(x)…

A: We have to find out derivative

Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: To find f'(a) & equation of tangent:

Q: Given the following vector field and oriented curve C, evaluate F = (x,y) on the parabola r(t) =…

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Q: Find the distance between the pair of points (2.5,8.2) and (-0.5,5.2). If necessary, express the…

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Q: Solve the given initial-value problem. y" + 6y'7y= 11e²x, y(0) = 1, y'(0) = 1

A: Given :y''+6y'-7y=11e2x

Q: Determine the intervals on which f'(x) is positive and negative, assuming that given figure is the…

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Q: (B): If A = 2i +3j - 4k; B = 3i - 4j+5k and C = i + j - k, find: (iii)A. (B+C)and (A + B).C (iv)…

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Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) dx ; (2) f sin x+cos x dx sin³ x…

A: We will use partial fraction to solve the first part of the question.

Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A: I have stated the used formulas in the solution

Q: Find the slopes of the surface in the x- and y-directions at the given point. h(x, y) = x2 − y2 (-2,…

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Q: A. Find the following limits. Answer four only. x-¹-1 i. ii. iii. lim- X-1 X-1 lim 4x-x² X-4 2-√√x…

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Q: Use the substitution u = 3x²-2 to find the following indefinite integral. Check your answer by…

A: We need to find integral.

Q: Q / if w = tan x and x=4²++ Find dw dt

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Q: Compute u v if u and v are unit vectors and the angle between them is

A: topic- dot product of vectors

Q: Consider the region depicted in the following figure. Find the area of R. -1 YA 4- 3+ 2 1 0 -1. f(x)…

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Q: In Exercises 37-42, use the Shell Method to find the volume obtained by rotating region A in Figure…

A: See this solution in below

Q: Q5: Find dx (1) In(x - y) = xy + y² : (4) y = x sinh 2x-cosh 2x for the following functions: (2) y =…

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Q: Solve the given initial-value problem. y(x) = y" + 6y'7y = 11e2x, y(0) = 1, y'(0) = 1 -7.x 11e2x 7e…

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