{"id":4292,"date":"2018-04-18T04:46:39","date_gmt":"2018-04-18T04:46:39","guid":{"rendered":"https:\/\/www.helpingstudents.com.ng\/?p=4292"},"modified":"2023-12-04T22:04:21","modified_gmt":"2023-12-04T22:04:21","slug":"questions-on-integration-and-vector-algebra","status":"publish","type":"post","link":"https:\/\/hstutorial.com\/de\/questions-on-integration-and-vector-algebra\/","title":{"rendered":"Fragen zur Integration und Vektoralgebra"},"content":{"rendered":"<p><strong>Integration<\/strong> is another aspect of calculus. It is sometimes called anti-differentiation because it is the reverse of differentiation. You can attempt up to <a href=\"https:\/\/hstutorial.com\/de\/22-questions-on-differentiation\/\">22 questions on differentiation by clicking on this link.<\/a><\/p>\n<blockquote><p>Subscribe to our YouTube channel so as not to miss a tutorial video.<\/p>\n<p><script src=\"https:\/\/apis.google.com\/js\/platform.js\"><\/script><\/p>\n<div class=\"g-ytsubscribe\" data-channelid=\"UCsHPKTWR8pDErG0onuksKSA\" data-layout=\"full\" data-count=\"default\"><span style=\"font-size: 16px;\">\u00a0<\/span> <span style=\"background-color: #ffffff; font-size: 16px;\">\u00a0<\/span><\/div>\n<\/blockquote>\n<h2><strong>What is Vector Algebra?<\/strong><\/h2>\n<p>A Vector is a quantity having both magnitude and direction. And since you can&#8217;t talk about Vector without mentioning Scalar, it would be good to note that Scalar is a quantity that has magnitude but one direction. <strong>(<em>kindly use the comment box below to ask a question<\/em>).<\/strong><\/p>\n<h3>Questions on Integration<\/h3>\n<ol>\n<li>The gradient of a curve passing through the point (3,1) is given by:<\/li>\n<\/ol>\n<p>dy\/dx = x<sup>2 <\/sup>\u2013 4x + 3<\/p>\n<p>Find the equation of the curve and the area enclosed by the curve, the maximum and minimum ordinates and the x-axis.<\/p>\n<ol start=\"2\">\n<li>The marginal revenue of a firm is found to be 15 \u2013 4q. Determine the revenue function if from past sales the revenue was N1,250 when 28 units of the product were sold.<\/li>\n<\/ol>\n<ol start=\"3\">\n<li>If the marginal cost of producing a product in a firm is:<\/li>\n<\/ol>\n<p>MC = 5q<sup>2 <\/sup>\u2013 7q + 20,<\/p>\n<p>Find the total variable cost of producing the first 100 units of the product in the firm.<\/p>\n<ol start=\"4\">\n<li>Determine the customer&#8217;s surplus of a commodity at a price of N15 given that the demand function is p = 24 \u2013 q<sup>2<\/sup>.<\/li>\n<\/ol>\n<ol start=\"5\">\n<li>If the demand function for a product is p = 155 \u2013 3q and the supply function is p = 7q \u2013 20<\/li>\n<\/ol>\n<p>Find:<\/p>\n<ul>\n<li>The equilibrium price and quantity.<\/li>\n<li>The consumer\u2019s surplus.<\/li>\n<li>The producer\u2019s surplus.<\/li>\n<\/ul>\n<h3>Questions on Vector Algebra<\/h3>\n<ol>\n<li>A security firm decides to sell four of its stocks. If the shares are 200, 150, 300 and 250 for stocks A, B, C, and D respectively and the selling price per share N200 for A, N100 for B, N300 for C and N250 for stock D. Calculate the total receipts from the stocks.<\/li>\n<\/ol>\n<ol start=\"2\">\n<li>Raphael Investment Limited decides to sell three of its stock. 300 shares of stock P, 400 shares of stock Q and 200 shares of stock R were sold. The selling price per share was N10, N8, and N5 respectively. Determine the total amount received from the sales of the stock.<\/li>\n<\/ol>\n<ol start=\"3\">\n<li>If <u>A<\/u> = 3<u>i<\/u> \u2013 2<u>J<\/u> + <u>k<\/u> and\u00a0\u00a0<u>B<\/u> = 2<u>i<\/u> + 3<u>J<\/u> \u2013 4<u>k<\/u><\/li>\n<\/ol>\n<p>Find:<\/p>\n<ul>\n<li><u>A<\/u> . <u>B<\/u> and angle between the vectors <u>A<\/u> and <u>B<\/u><\/li>\n<li><u>A<\/u> x <u>B<\/u><\/li>\n<li>|<u>A<\/u>| and |<u>B<\/u>|<\/li>\n<li>Hence find the angle between the vectors.<\/li>\n<\/ul>\n<ol start=\"4\">\n<li>Find the vector product of the following:<\/li>\n<\/ol>\n<ul>\n<li><u>A<\/u> = 2<u>i<\/u> + <u>J<\/u> and\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <u>b<\/u> = <u>I<\/u> -3<u>J<\/u> + <u>K<\/u><\/li>\n<li>(8,4,2) and\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (6,4,-3)<\/li>\n<\/ul>\n<ol start=\"5\">\n<li>If <u>r<\/u> = 3<u>i<\/u> \u2013 2<u>J<\/u> + <u>k<\/u><\/li>\n<\/ol>\n<ul>\n<li>Find the magnitude <u>r<\/u><\/li>\n<li>Find the unit vector in the direction of <u>r<\/u><\/li>\n<li>Calculate the direction cosine of <u>r<\/u>.<\/li>\n<\/ul>\n<ol start=\"6\">\n<li>Show that p and q are perpendiculars where:<\/li>\n<\/ol>\n<p><u>P<\/u> = 3<u>i<\/u> \u2013 4 <u>J<\/u> + 5<u>k<\/u>\u00a0\u00a0\u00a0\u00a0 and<\/p>\n<p><u>q<\/u> = 2<u>i<\/u> + <u>J<\/u> + 2<u>k<\/u><\/p>\n<h2>Other Mathematics Questions<\/h2>\n<ol>\n<li><a href=\"https:\/\/hstutorial.com\/de\/questions-on-coordinate-geometry\/\">Koordinatengeometrie<\/a><\/li>\n<li><a href=\"https:\/\/hstutorial.com\/de\/questions-on-permutation-and-combination\/\">Permutation and Combination<\/a><\/li>\n<li><a href=\"https:\/\/hstutorial.com\/de\/questions-on-set-theory\/\">Mengenlehre<\/a><\/li>\n<li><a href=\"https:\/\/hstutorial.com\/de\/questions-on-probability-business-maths\/\">Empirische Wahrscheinlichkeit<\/a><\/li>\n<li><a href=\"https:\/\/hstutorial.com\/de\/questions-on-integration-and-vector-algebra\/\">Integration &amp; Vector Algebra<\/a><\/li>\n<li><a href=\"https:\/\/hstutorial.com\/de\/22-questions-on-differentiation\/\">Differenzierung<\/a><\/li>\n<\/ol>\n<h3>HS Tutorial on YouTube<\/h3>\n<p><span class=\"waslinkname\">Click here to see some of our Mathematics videos on YouTube.<\/span><\/p>","protected":false},"excerpt":{"rendered":"<p>Die Integration ist ein weiterer Aspekt der Infinitesimalrechnung. Sie wird manchmal als Antidifferenzierung bezeichnet, weil sie das Gegenteil der Differenzierung ist. Sie k\u00f6nnen bis zu 22 Fragen zur Differenzierung beantworten, indem Sie auf ... klicken.<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/hstutorial.com\/de\/questions-on-integration-and-vector-algebra\/\"> <span class=\"screen-reader-text\">Fragen zur Integration und Vektoralgebra<\/span> Weiterlesen &raquo;<\/a><\/p>","protected":false},"author":2,"featured_media":4566,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"footnotes":""},"categories":[55],"tags":[229,170],"class_list":["post-4292","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-exam-questions","tag-business-maths","tag-past-questions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.5 (Yoast SEO v21.5) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Questions on Integration and Vector Algebra - HS Tutorial<\/title>\n<meta name=\"description\" content=\"Integration is another aspect of calculus. 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