TE 2 1² sinº x cos² x dx 0

Q: If f'(x) = 2x³ + 3x² − 4x + 5 and f(0) = 1 and f'(0) = 2 find f.

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Q: Find the direction derivative of f(x,y)= Xe ² + y ² at the paint (2,1), by the dirction of V = i- j

A: Topic:- application of derivatives

Q: Q1) L-1 s(s²-1) = a) cosht-1 Q2) The general solution of y"" + 2y"-y' - 2y = 0, is: a) y(x) = c₁e²x…

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Q: Evaluate using Partial Fraction Decomposition: S x2 (x+1)²(x-1) -dx

A: We know, ∫dxx-a=lnx-a, for any real number a ∫dxxn=x1-n1-n, for any real number n.

Q: Evaluate 1¹ 1 - cos 2x sin 2x dx In | csc 2x + cot 2x | -ln | sin 2x | +C In 1|csc 2x-cot 2x |--In |…

A: The given integral is: I=∫1-cos2xsin2x   As we know the common integrals; 1). ∫cscxdx=lncscx-cotx+C…

Q: x(t) = 4+ t Find a plane through the point (-1,5,-3) and orthogonal to the line y(t) = 3 - 6t z(t) =…

A: This question can be solved using the concept of lines and planes.

Q: x(t) = Find a plane containing the point (-3,5,-2) and the line y(t) = z(t) = 5 - 3t 8 + 6t 7 + 6t

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Q: Find an equation for the line tangent to the graph of y = tan ¹ (2x) 2 1 What is the tangent line to…

A: As we know that; The slope of the tangent line to the given curve is equal to the first derivative…

Q: Solve the integral shown below. Show your solutions. 3xe ²x dx

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Q: Given that f(x) = (x - 2)² and g(x) = 1 - 3x, find (a) (f + g)(4)= (b) (f - g)(4)= (c) (fg)(4)= (d)…

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Q: Determine the sum of the following series. NOTE: Enter the exact, simplified answer as improper…

A: We have to find the sum

Q: Question 4 (a) Solve the following: √4x² dx (b) Explain with the aid of a sketch how this value can…

A: Let's solve given integral.

Q: Find the Jacobian for z = ² + 8uv and y = 6uv². Jacobian (equation format)

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Q: Question 4 (a) Solve the following: (b) Explain with the aid of a sketch how this value can be…

A: Above question is solved.

Q: 5 ;ㅣ

A: We have to find first four terms of give series.

Q: Find the arclength of the curve y = MIN M on [0,4].

A: See the details solution in below

Q: Q3) Given, u (x, y) = xy is harmonic, find a harmonic conjugate v(x, y), write u+iv as a function of…

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Q: Find the Volume: Rotate the region bounded by y = 7 - x², x = -2 and x = 2 and the x-axis about the…

A: Volume of the solid of Revolution :  Suppose y=f(x) is a continuous non-negative function on the…

Q: (e) If f and g are differentiable then, d -f(g(x)) = f'(g(x))g'(x) dx True False

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Q: Find the area bounded by the given curves.

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Q: dh dt k √h(t) ||| h(0) = 2 2 ● T.V

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Q: Solve the integral shown below. . S | xsin xdx

A: Given problem:- ∫x sin(x)dx

Q: A while than 15t 7-47 / र

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Q: The distance between the points (-8, m) and (m, 9) is 13. What are the possible values of m? a) 3 or…

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Q: Let a, be such that asb. Prove that tx Eqt ax cbx

A: Concept: We have a,b∈Q means that a, and b belongs to the rational numbers and a<b means that a…

Q: Part One. Multiple Choice 1. Which of the following is not a true statement about limits? a) A limit…

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Q: KIN T 2 sin² x cos⁹ x dx

A: We will solve integral using Wallis formula  The wallis formula is :

Q: 6 Find the area enclosed by the given curves. * y = x³ and y = 4x

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: 15. f (sec² x) dx / (√(1-4 tan² x))

A: Hi and thanks for your question! Unfortunately, as per our guideline, only one question should be…

Q: Find the constants a and b such that the function is differentiable everywhere. x²-9 x+3 if x < -3…

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Q: Q4: Evaluate the following integral. 7/21/2 sin y 5% dy dx Y

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Q: Vectors [2, 5, a] and [-6, b, 9] are collinear. What is the value of ? a a) 5 b) -3 Oc) -5 d) 3

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Q: 6. f(x-1) dx/(x+1)

A: **As per our guidelines, we are supposed to answer only one question at a time. So, we will solve…

Q: Solve the integral shown below. So cos¹¹ 3xdx Só 11

A: ∫0π6cos113xdxLet u=3x.=∫0π2cos11u13du=13·∫0π2cos11udu=13·∫0π21-sin2u5cosuduLet…

Q: Determine the value(s) of k for which the following planes will intersect in a lin x+y+z=0 2x + 3y -…

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Q: Integral Calculus

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Q: True or false: If {(2, 1-z, z+3)} is the solution set of a system with dependent equations, then (0,…

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Q: Solve the following initial value problem for r as a function of t d²r Differential equation:…

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Q: Let u = (a11, a12, a13), v = (a21, a22, a23), w = (a31, a32, a33) be three vectors in R³. Explain,…

A: let  x, y, z  be the non zero  vector that is orthogonal to   u, v and w

Q: Find the limit or show that it does not exist. lim x - √x 818

A: follow next step

Q: (4) Use logarithmic differentiation to find the derivative of the following function. y = x¹/x

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Q: 9. Find f(x) and g(x) so the function can be expressed as y = f(g(x)). 8 y = +4 2 X

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Q: y' 1+x² x Y

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Q: l₁: x = 7+2t, y = 2 + t, z = -6 - 3t y-9 Z-13 l₂: 3 - x = -5 -5

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Q: A manufacturer has modeled its yearly production function P (the monetary value of its entire…

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Q: 3. Find the volume of the solid that lies under the paraboloid 5z = x² + y², above the xy-plane, and…

A: To find the volume of the solid that is bounded by given curves.

Q: 4.1 Evaluate the integral [3√x √(3√x - 1 / +5 4 + x² expressions after applying the integration…

A: We have to evaluate the integral

Q: lim √25t2 + 2-5t

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Q: cos-¹(2x+5), then dom(f) = = If f(x) = x+3 (A) (-3,-2) L (B) [-3, -2] (C) (-3, -2] (D) (-1,1) (E)…

A: Doamin of a function:- It the set of input values where the function at the values…

Q: 20. Stan² x dx

A: Consider the integral  ∫tan2x dx